Question

solve the system of equations

x=6y-3
2x+7y=13

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we will use the substitution method.

First, rearrange the first equation to solve for x in terms of y:
x = 6y - 3

Next, substitute this expression for x in the second equation:
2(6y - 3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1

Now, substitute this value of y back into the first equation to solve for x:
x = 6(1) - 3
x = 6 - 3
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 1.

Answer 2

solve the system of equations

8x-3y= - 22

y=10+4x

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we will use the substitution method.

First, rearrange the second equation to solve for y in terms of x:
y = 10 + 4x

Next, substitute this expression for y in the first equation:
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = 8
x = -2

Now, substitute this value of x back into the second equation to solve for y:
y = 10 + 4(-2)
y = 10 - 8
y = 2

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

Answer 4

solve the system of equations

5x+2y=14
x-6y=22

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of elimination.

First, let's multiply the second equation by 5 to make the coefficients of x in both equations equal:
5(x-6y)=5(22)
5x-30y=110

Now we can subtract the first equation from this new equation:
(5x-30y)-(5x+2y)=110-14
5x-30y-5x-2y=96
-32y=96
y=96/(-32)
y=-3

Substitute this value of y into the first equation:
5x+2(-3)=14
5x-6=14
5x=20
x=20/5
x=4

Therefore, the solution to the system of equations is x = 4 and y = -3.

Answer 6

solve the system of equations

-9x+y=12
2x+4y=-28

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of elimination.

First, let's multiply the first equation by 4 and multiply the second equation by -1 to make the coefficients of y in both equations equal:
4(-9x+y)=4(12)
-36x+4y=48

-1(2x+4y)=-1(-28)
-2x-4y=28

Now, we can add these two new equations together to eliminate y:
(-36x+4y)+(-2x-4y)=48+28
-38x = 76
x = 76/(-38)
x = -2

Substitute this value of x into one of the original equations. Let's use the first equation:
-9(-2) + y = 12
18 + y = 12
y = 12 -18
y = -6

Therefore, the solution to the system of equations is x = -2 and y = -6.

Answer 8

solve the system of equations

y=2 + 3x

4x-3y=-16

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of substitution.

First, we'll substitute the expression for y from the first equation into the second equation:
4x - 3(2 + 3x) = -16

Next, distribute -3 to each term inside the parentheses:
4x - 6 - 9x = -16

Combine like terms:
-5x - 6 = -16

Add 6 to both sides:
-5x = -10

Divide both sides by -5:
x = 2

Now substitute the value of x back into the first equation to solve for y:
y = 2 + 3(2)
y = 2 + 6
y = 8

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

Answer 10

solve the system of equations

2x+6y=-18

x=5y-1

Answer 11

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of substitution.

First, we substitute the expression for x from the second equation into the first equation:

2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1

Now that we have the value of y, we can substitute it back into the second equation to solve for x:

x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations is x = -6 and y = -1.

Answer 12

solve the system of equations

3x+y=2
7x-4y+30

Answer 13

[AI-generated answer — Bot GPT 3.5]

I apologize, but it seems there is a missing "=" sign in the second equation. Could you please provide the complete second equation?

Answer 14

solve the system of equations

3x+y=2
7x-4y=30

Answer 15

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of substitution or elimination. Let's use elimination.

First, let's multiply the first equation by 4 to make the coefficients of y in both equations equal:
4(3x + y) = 4(2)
12x + 4y = 8

Now, we can subtract the second equation from this new equation:
(12x + 4y) - (7x - 4y) = 8 - 30
12x + 4y - 7x + 4y = -22
5x + 8y = -22 (Equation 3)

We can now solve this new equation (Equation 3).

Now, let's multiply the first equation by 7 and the second equation by 3 to make the coefficients of x in both equations equal:
7(3x + y) = 7(2)
21x + 7y = 14 (Equation 4)

3(7x - 4y) = 3(30)
21x - 12y = 90 (Equation 5)

We can now subtract Equation 5 from Equation 4 to eliminate x:
(21x + 7y) - (21x - 12y) = 14 - 90
21x + 7y - 21x + 12y = -76
19y = -76
y = -76/19
y = -4

Now, substitute this value of y into Equation 1:
3x + (-4) = 2
3x - 4 = 2
3x = 2 + 4
3x = 6
x = 6/3
x = 2

Therefore, the solution to the system of equations is x = 2 and y = -4.

Answer 16

solve the system of equations

-4x+6y=38
x-5y=-20

Answer 17

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we will use the method of substitution.

First, rearrange the second equation to solve for x in terms of y:
x = 5y - 20

Next, substitute this expression for x in the first equation:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = -42/(-14)
y = 3

Now, substitute this value of y back into the second equation to solve for x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5

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

Answer 18

How many solutions does the system of equations have.

-5x+y=-18
10x-2y=36

Answer 19

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions the system of equations has, we need to analyze the consistent property and the independent property of the system.

First, let's rewrite the equations in standard form:

-5x + y = -18
10x - 2y = 36

To find the number of solutions, let's compare the slopes of the equations. The first equation has a slope of -5/1, and the second equation has a slope of 10/2, which simplifies to 5.

Since the slopes are different, the lines are not parallel, and they will intersect at a single point. Therefore, the system has one solution.

In conclusion, the system of equations has one solution.