Question

Given the equations:

y = -4x + 10
y = 2x - 8

What are the solutions to this system of equations?

A. x = 3, y = -2
B. x = -3, y = -14
C. x = -1, y = 2
D. x = 1, y = -2

Answer 1

The solution to the system of equations is found by setting the two equations equal to each other and solving for x, then substituting the value of x back into one of the equations to find y. The solution is x = 3, y = -2, which corresponds to option A.

Step-by-step explanation:

To find the solution to the system of equations, we can set the equations y = -4x + 10 and y = 2x - 8 equal to each other since they both equal y. Doing so, we get:

-4x + 10 = 2x - 8

This simplifies to:

-4x - 2x = -8 - 10

-6x = -18

Dividing both sides of the equation by -6 gives us:

x = 3

Now, we substitute x = 3 into one of the original equations to solve for y:

y = -4(3) + 10 = -12 + 10 = -2

Therefore, the solution to the system of equations is x = 3, y = -2, which is option A.