Find the solution to the system of equations by substitution.
--4x + y = 14 -5x + 8y = 4
A) (-2, -4)
B) (-3, -3)
C) (-4, -2)
D) no solution

Question

Quizplus · Accepted Answer

Solve the first equation for y: y = 4x + 14. 
Substitute it into the second equation and solve for x: -5x + 8(4x + 14) = 4. 
Simplify and solve for x: x = -4. 
Substitute x = -4 into y = 4x + 14 and solve for y: y = -2. 
So the solution is (-4, -2). Therefore, the correct choice is C. We can solve for y in the first equation: 
y = 4x + 14 
Then substitute this expression for y into the second equation: 
-5x + 8(4x+14) = 4 
-5x + 32x + 112 = 4 
27x = -108 
x = -4 
Finally, substitute this value into either of the original equations to solve for y: 
-4(-4) + y = 14 
y = -2 
Thus, the solution is (-4, -2), which corresponds to choice C.

Find the Solution to the System of Equations by Substitution