Question

is (5,-1) a solution to the system of these linear equations: x+y=4 and 2x+3y=7 and why?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To check if (5,-1) is a solution to the system of linear equations, we substitute the values of x and y into each equation and see if both equations are satisfied:

For the first equation x + y = 4:
Substituting x=5 and y=-1, we get:
5 + (-1) = 4
4 = 4

The first equation is satisfied.

For the second equation 2x + 3y = 7:
Substituting x=5 and y=-1, we get:
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7

The second equation is also satisfied.

Since both equations are satisfied when x=5 and y=-1, the point (5,-1) is indeed a solution to the system of linear equations.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if (5, -1) is a solution to the system of linear equations, we can substitute the values of x and y into both equations and check if the resulting equations are true.

Let's check the first equation: x + y = 4
Substituting x = 5 and y = -1:
5 + (-1) = 4
4 = 4

The equation is true for the values x = 5 and y = -1.

Now let's check the second equation: 2x + 3y = 7
Substituting x = 5 and y = -1:
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7

The equation is also true for the values x = 5 and y = -1.

Since both equations are true when values x = 5 and y = -1, we can conclude that (5, -1) is indeed a solution to the system of linear equations.

Answer 3

[AI-generated answer — Explain Bot]

To determine whether (5, -1) is a solution to the system of linear equations, we need to substitute the values of x and y into both equations and check if the equations hold true.

First, let's substitute x = 5 and y = -1 into the first equation:
5 + (-1) = 4
4 = 4

The equation holds true, as both sides are equal. This means that (5, -1) satisfies the first equation.

Now, let's substitute x = 5 and y = -1 into the second equation:
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7

Here again, the equation holds true, as both sides are equal. This means that (5, -1) satisfies the second equation.

Since (5, -1) satisfies both equations, it is indeed a solution to the system of linear equations.

Answer 4

is (7,3) a solution to the system of these linear equations: 3x+2y=5 and -x+6y=11 and why?

Answer 5

[AI-generated answer — Bot GPT 3.5]

To check if (7,3) is a solution to the system of linear equations, we substitute the values of x and y into each equation and see if both equations are satisfied:

For the first equation 3x + 2y = 5:
Substituting x=7 and y=3, we get:
3(7) + 2(3) = 5
21 + 6 = 5
27 ≠ 5

The first equation is not satisfied.

For the second equation -x + 6y = 11:
Substituting x=7 and y=3, we get:
-(7) + 6(3) = 11
-7 + 18 = 11
11 = 11

The second equation is satisfied.

Since the first equation is not satisfied when x=7 and y=3, (7,3) is not a solution to the system of linear equations.

Answer 6

whats the solution to these linear equations: x-3y=18 and 7x-5y=46

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the solution to the system of linear equations x - 3y = 18 and 7x - 5y = 46, we can use the method of substitution or elimination.

Method of substitution:
From the first equation, we can express x in terms of y:
x = 3y + 18

Substituting x = 3y + 18 into the second equation:
7(3y + 18) - 5y = 46
21y + 126 - 5y = 46
16y + 126 = 46
16y = 46 - 126
16y = -80
y = -80/16
y = -5

Substituting the value of y = -5 into the expression for x from the first equation:
x = 3(-5) + 18
x = -15 + 18
x = 3

Therefore, the solution to the system of linear equations is x = 3 and y = -5.

Answer 8

what 2 linear equations have the solution (4,-3)

Answer 9

[AI-generated answer — Bot GPT 3.5]

Two linear equations that have the solution (4, -3) are:

1. x - y = 7
2. 2x + 3y = 2

To check that the solution (4, -3) satisfies both equations:

For the first equation x - y = 7, substituting x = 4 and y = -3 we get:
4 - (-3) = 7
4 + 3 = 7
7 = 7

The first equation is satisfied.

For the second equation 2x + 3y = 2, substituting x = 4 and y = -3 we get:
2(4) + 3(-3) = 2
8 - 9 = 2
-1 = 2

The second equation is not satisfied.

Since the second equation is not satisfied when x = 4 and y = -3, it cannot be said that (4, -3) is a solution to the system of linear equations.

Answer 10

what is the solution to the 2 linear equations -5x+4y=48 and -5x-8y=24

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the solution to the system of linear equations -5x + 4y = 48 and -5x - 8y = 24, we can use the method of elimination.

Subtracting the second equation from the first equation, we eliminate the term '-5x' on the left side of the equation:
(-5x + 4y) - (-5x - 8y) = 48 - 24
-5x + 4y + 5x + 8y = 24
12y = 24
y = 24/12
y = 2

Plugging the value of y = 2 back into either equation, we can solve for x. Let's use the first equation:
-5x + 4(2) = 48
-5x + 8 = 48
-5x = 48 - 8
-5x = 40
x = 40 / -5
x = -8

Therefore, the solution to the system of linear equations is x = -8 and y = 2.

Answer 12

what is the solution to the 2 linear equations 8x-4y=-28 and 2x-6y=8

Answer 13

[AI-generated answer — Bot GPT 3.5]

To find the solution to the system of linear equations 8x - 4y = -28 and 2x - 6y = 8, we can use the method of elimination.

First, let's multiply the second equation by -4 to create opposite coefficients for the x term:
-4(2x - 6y) = -4(8)
-8x + 24y = -32

Now, we can add the two equations together to eliminate the x term:
(8x - 4y) + (-8x + 24y) = -28 + (-32)
-4y + 24y = -60
20y = -60
y = -60/20
y = -3

Substituting y = -3 into the first equation:
8x - 4(-3) = -28
8x + 12 = -28
8x = -28 - 12
8x = -40
x = -40/8
x = -5

Therefore, the solution to the system of linear equations is x = -5 and y = -3.

Answer 14

For renting tables, Parties ‘R Us charges, C, a $60 delivery fee and $4 per table, T. Rob’s Rentals charges, C, a $40 delivery fee and $6 per table, T. Write the pair of linear equations that model this situation.

Answer 15

[AI-generated answer — Bot GPT 3.5]

Let's let C represent the total cost, and T represent the number of tables rented.

For Parties 'R Us:
The total cost, C, is equal to the delivery fee of $60 plus the cost per table, which is $4 per table:
C = $60 + $4T

For Rob's Rentals:
The total cost, C, is equal to the delivery fee of $40 plus the cost per table, which is $6 per table:
C = $40 + $6T

Therefore, the pair of linear equations that model this situation are:

Parties 'R Us: C = $60 + $4T
Rob's Rentals: C = $40 + $6T

Answer 16

The Lincoln High School Student Council wants to raise $300 to make a donation to a homeless shelter. To help the students earn the money, the principal has agreed to pay $15 for each member who picks up litter outside, P, , and $10 for each member who cleans the hallways, C. All 25 members of the student council will be participating. Write the pair of linear equations that model this situation.

Answer 17

[AI-generated answer — Bot GPT 3.5]

Let's let P represent the number of members who pick up litter outside and C represent the number of members who clean the hallways.

For picking up litter outside:
The total amount earned, A, is equal to the amount paid per member, which is $15, multiplied by the number of members who pick up litter, P:
A = $15P

For cleaning the hallways:
The total amount earned, A, is equal to the amount paid per member, which is $10, multiplied by the number of members who clean the hallways, C:
A = $10C

Since the goal is to raise $300, we can set up another equation:
A = $300

Therefore, the pair of linear equations that model this situation are:

For picking up litter: A = $15P
For cleaning the hallways: A = $10C
The goal: A = $300

Answer 18

Two boating charter companies operate out of a port. Maritime Voyage charges $250 for the boat rental and $25 per person. Catamaran Command charges $75 for the boat rental and $50 per person. If a group has 10 customers, which charter should they choose?

Answer 19

[AI-generated answer — Bot GPT 3.5]

To determine which charter company the group should choose, we need to calculate the total cost for each company based on the given information.

For Maritime Voyage:
The boat rental cost is $250 and they charge $25 per person.
So, the total cost for Maritime Voyage can be calculated as:
Total Cost = Boat Rental Cost + (Number of Customers * Cost per Person)
Total Cost = $250 + (10 * $25) = $250 + $250 = $500

For Catamaran Command:
The boat rental cost is $75 and they charge $50 per person.
So, the total cost for Catamaran Command can be calculated as:
Total Cost = Boat Rental Cost + (Number of Customers * Cost per Person)
Total Cost = $75 + (10 * $50) = $75 + $500 = $575

Comparing the total costs, we can see that Maritime Voyage has a total cost of $500, while Catamaran Command has a total cost of $575.

Therefore, the group of 10 customers should choose the Maritime Voyage charter company as it has the lower total cost.

Answer 20

the point (0-2) is a solution to which system:

A x+y=2 and -x+2y=16
B -5x+y=-2 and -3x+6y=-12
C -4x+y=6 and -5x-y=21
D -5x=y-3 and 3x-8y=24

Answer 21

[AI-generated answer — Bot GPT 3.5]

To determine if the point (0, -2) is a solution to a given system of equations, we substitute the x and y values into each equation and check if the equations are satisfied.

For system A:
Substituting x = 0 and y = -2 into the equations:
0 + (-2) = 2 -> -2 = 2 (Not satisfied)
-0 + 2(-2) = 16 -> 0 - 4 = 16 -> -4 = 16 (Not satisfied)

The point (0, -2) is not a solution to system A.

For system B:
Substituting x = 0 and y = -2 into the equations:
-5(0) + (-2) = -2 -> -2 = -2 (Satisfied)
-3(0) + 6(-2) = -12 -> 0 - 12 = -12 -> -12 = -12 (Satisfied)

The point (0, -2) is a solution to system B.

For system C:
Substituting x = 0 and y = -2 into the equations:
-4(0) + (-2) = 6 -> -2 = 6 (Not satisfied)
-5(0) - (-2) = 21 -> 0 + 2 = 21 -> 2 = 21 (Not satisfied)

The point (0, -2) is not a solution to system C.

For system D:
Substituting x = 0 and y = -2 into the equations:
-5(0) = -(-2) - 3 -> 0 = 2 - 3 -> 0 = -1 (Not satisfied)
3(0) - 8(-2) = 24 -> 0 + 16 = 24 -> 16 = 24 (Not satisfied)

The point (0, -2) is not a solution to system D.

Therefore, the point (0, -2) is only a solution to system B.

Answer 22

how many solutions does the system y = 5x + 7 and 3y - 15x = 18 have?

Answer 23

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for the given system of equations, we can compare the slopes of the two equations.

The given equations are:

1. y = 5x + 7
2. 3y - 15x = 18

Equation 1 is in slope-intercept form (y = mx + b) with a slope of 5. Equation 2 is in standard form (Ax + By = C), so we need to rearrange it to slope-intercept form:

3y - 15x = 18
3y = 15x + 18
y = 5x + 6

Both equations have the same slope (5), indicating that the lines are parallel. Parallel lines have no points of intersection and, therefore, no solutions.

Hence, the system y = 5x + 7 and 3y - 15x = 18 has no solutions.

Answer 24

how many solutions does the system y = 3x + 6 and y = -13x - 4 have?

Answer 25

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for the given system of equations, we will compare the slopes and y-intercepts of the two equations.

The given equations are:
1. y = 3x + 6
2. y = -13x - 4

Both equations are in slope-intercept form (y = mx + b) and have different slopes. Equation 1 has a slope of 3, while Equation 2 has a slope of -13.

Since the slopes of the two lines are different, they will intersect at a single point. This means that the system of equations has one unique solution.

Hence, the system y = 3x + 6 and y = -13x - 4 has one solution.

Answer 26

how many solutions does the system x - 2y = 6 and 3x - 6y = 18 have?

Answer 27

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for the given system of equations, we can check if the two equations are equivalent or independent.

The given equations are:

1. x - 2y = 6
2. 3x - 6y = 18

We can simplify the second equation by dividing both sides by 3:

2. x - 2y = 6

As we can see, both equations are equivalent. This means that they represent the same line and have infinitely many solutions. Any value of x and y that satisfies one equation will also satisfy the other equation.

Therefore, the system x - 2y = 6 and 3x - 6y = 18 has infinitely many solutions.

Answer 28

how many solutions does the system y = 23x - 1 and y = 23x - 2 have?

Answer 29

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for the given system of equations, we can compare the equations and see if they are equivalent or independent.

The given equations are:

1. y = 23x - 1
2. y = 23x - 2

Both equations have the same slope of 23 and the same y-intercept of -1 and -2, respectively. This indicates that the lines are parallel.

Parallel lines have the same slope but different y-intercepts, which means they will never intersect. Therefore, the system of equations has no solutions.

Hence, the system y = 23x - 1 and y = 23x - 2 has no solutions.

Answer 30

Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.

What equation represent how much money Judy will have in total after saving for D days?

What equation represents how much money Elenore will have in total after saving for D days?

What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved?

After the number of days it took both to have the same amount of money saved, how much money do they have each?

Answer 31

[AI-generated answer — Bot GPT 3.5]

The equation representing how much money Judy will have in total after saving for D days can be derived using the formula for linear growth:

Total money

Answer 32

Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.

give answers to all these questions below using the context of the sentence above

What equation represent how much money Judy will have in total after saving for D days?

What equation represents how much money Elenore will have in total after saving for D days?

What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved?

After the number of days it took both to have the same amount of money saved, how much money do they have each?

Answer 33

Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.

What equation represent how much money Judy will have in total after saving for D days?