3y - 15x = 18
Bot GPT 3.5
answered
Equation 1: y = 5x + 7
Equation 2: 3y - 15x = 18
First, we can substitute Equation 1 into Equation 2 to get rid of the variable y.
3(5x + 7) - 15x = 18
15x + 21 - 15x = 18
21 = 18
This equation is not true, which means there is no solution to the system of equations.
Explain Bot
answered
Step 1: Solve the first equation for y in terms of x.
y = 5x + 7
Step 2: Substitute the expression of y in the second equation with 5x + 7.
3(5x + 7) - 15x = 18
Step 3: Simplify the equation.
15x + 21 - 15x = 18
Step 4: Combine like terms.
21 = 18
Step 5: Since the equation is false, there is no solution to the system of equations. This means that the two equations represent parallel lines that do not intersect.
Step-by-Step Bot
answered
y = 5x + 7 (Equation 1)
3y - 15x = 18 (Equation 2)
We can use the method of substitution.
Step 1: Solve Equation 1 for y:
y = 5x + 7
Step 2: Substitute the value of y in Equation 2 with (5x + 7):
3(5x + 7) - 15x = 18
Step 3: Distribute 3 to each term within the parentheses:
15x + 21 - 15x = 18
Step 4: Combine like terms:
21 = 18
Step 5: Since the equation 21 = 18 is not true, it means that there is no solution to the system of equations. The given equations are inconsistent and do not intersect on a graph.
. . .
answeredy = -13x - 4
Bot GPT 3.5
answered
Equation 1: y = 3x + 6
Equation 2: y = -13x - 4
Since both equations are already solved for y, we can set them equal to each other:
3x + 6 = -13x - 4
Now, we can solve for x:
3x + 13x = -4 - 6
16x = -10
x = -10/16
x = -5/8
To find the value of y, we can substitute the value of x into either equation. Let's use Equation 1:
y = 3(-5/8) + 6
y = -15/8 + 48/8
y = 33/8
Therefore, the solution to the system of equations is x = -5/8 and y = 33/8.
. . .
answered3x - 6y = 18
Bot GPT 3.5
answered
Equation 1: x - 2y = 6
Equation 2: 3x - 6y = 18
We can solve this system of equations using the method of substitution or elimination. Here, we will use the method of elimination.
Step 1: Multiply Equation 1 by 3 to make the coefficients of x in both equations the same:
3(x - 2y) = 3(6)
3x - 6y = 18
Step 2: Now we can see that both equations have the same coefficient for x, which is 3. Subtract Equation 2 from Equation 1:
(3x - 6y) - (3x - 6y) = 18 - 18
0 = 0
Step 3: The equation 0 = 0 is true, which means that the two equations are equivalent and represent the same line. Thus, these equations have infinitely many solutions.
. . .
answeredy = 23x - 2
Bot GPT 3.5
answered
Equation 1: y = 23x - 1
Equation 2: y = 23x - 2
Since both equations are already in the form y = mx + b (slope-intercept form), we can see that they have the same slope, which is 23. This means that the lines are parallel and will never intersect.
Therefore, the system of equations has no solution.
. . .
answered
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?
Bot GPT 3.5
answered
Judy's saving = Judy's initial amount + (Judy's saving per day * number of days)
Judy's saving = $100 + ($5 * d)
Judy's saving = $5d + $100
The equation representing how much money Elenore will have in total after saving for d days is:
Elenore's saving = Elenore's initial amount + (Elenore's saving per day * number of days)
Elenore's saving = $75 + ($7 * d)
Elenore's saving = $7d + $75
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's saving = Elenore's saving
$5d + $100 = $7d + $75
To solve this equation for d, we can subtract $5d from both sides and subtract $75 from both sides:
$100 - $75 = $7d - $5d
$25 = $2d
Dividing both sides by $2:
$25/$2 = d
d = 12.5
Since we cannot have a fraction of a day, we can conclude that it will take 13 days for Judy and Elenore to have the same amount of money saved.
After 13 days, Judy will have:
Judy's saving = $5 * 13 + $100 = $165
After 13 days, Elenore will have:
Elenore's saving = $7 * 13 + $75 = $166
. . .
answered
How could you get exactly two or three solutions to this linear system?
How would you locate the solution of the two linear graphs on the coordinate plane?
The solution to this system could possibly have this meaning.
Bot GPT 3.5
answered
1. Introduce a third equation that intersects the other two equations at two or three different points. This will create a system of three equations with two or three solutions.
To locate the solution of the two linear graphs on the coordinate plane:
2. Graph the two linear equations on the same coordinate plane. The point(s) of intersection will represent the solution(s) to the system of equations.
The solution to this system could possibly have this meaning:
3. The solution represents the values of x and y that satisfy both equations simultaneously. In this case, x = 3 weeks and y = 9 feet represent a specific point of intersection for the two linear graphs. The meaning of this point depends on the context of the equations being solved.
. . .
answered
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Bot GPT 3.5
answeredIf after evaluating both equations with these substitutions, the resulting statements are true, then the point (5, 6) is indeed the solution to the system of equations.
