3x - 8y = -17 2x -7y = -18

6x - 16y =-34

-6x +21y =54

5y=20

y=4

2x-7y =-18
2x -7(4)=-18
2x - 28=-18
2x=10
x=5

Correct answer

To find the solution to this system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method to solve it step by step.

Step 1: Multiply the second equation by 3 to make the coefficients of x in both equations the same. This will allow us to eliminate the x variable when we subtract the equations.
3(2x - 7y) = 3(-18)
This simplifies to:
6x - 21y = -54

Step 2: Now, subtract the first equation from the equation obtained in Step 1. This will eliminate the x variable.
(6x - 21y) - (3x - 8y) = -54 - (-17)
Simplifying the equation gives us:
6x - 21y - 3x + 8y = -54 + 17
Combining like terms, we get:
3x - 13y = -37

Step 3: Now, we have a new equation:
3x - 13y = -37

Step 4: Solve the new equation for x or y. Let's solve for x.
3x = -37 + 13y
Divide both sides by 3:
x = (-37 + 13y) / 3

Step 5: Substitute the expression for x in terms of y into one of the original equations. Let's use the first equation:
3((-37 + 13y) / 3) - 8y = -17
Multiply through by 3 to eliminate the fraction:
-37 + 13y - 8y = -51
Combine like terms:
5y = -14
Divide by 5:
y = -14 / 5
y = -2.8

Step 6: Substitute the value of y into the expression for x:
x = (-37 + 13(-2.8)) / 3
Simplify the expression:
x = (-37 - 36.4) / 3
Combine like terms:
x = -73.4 / 3
x ≈ -24.467

So, the solution to the system of equations is x ≈ -24.467 and y = -2.8.