Final answer:
The solution to the given system of equations is (x, y) = (13, -20).
Step-by-step explanation:
The given system of equations is:
2x = -y + 6
-4x + 3y = 8
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable:
6x = -3y + 18
-8x + 6y = 16
Add the two equations:
(6x + -8x) + (-3y + 6y) = 18 + 16
-2x + 3y = 34
Simplify the equation:
-2x + 3y = 34
We now have a new system of equations:
-2x + 3y = 34
-4x + 3y = 8
Subtract the second equation from the first equation:
(-2x + 3y) - (-4x + 3y) = 34 - 8
2x = 26
Divide both sides by 2:
x = 13
Substitute the value of x into one of the original equations to solve for y:
2(13) = -y + 6
26 = -y + 6
Subtract 6 from both sides:
20 = -y
Divide both sides by -1:
y = -20
Therefore, the solution to the system of equations is (x, y) = (13, -20).