Question

What is the solution of the following system? Use the elimination method.

−4x+y=−6
−8x−2y=14
​

A) The only solution is (0, -3/2).
B) The only solution is (0, -6).
C) There are an infinite number of solutions.
D) There is no solution.

Answer 1

To solve the system of equations using the elimination method, multiply the first equation by 2 to eliminate the x variable. Then, add the two equations together to solve for x. Substitute the value of x into the first equation to solve for y. The solution is (x, y) = (-1/8, -25/2).

Step-by-step explanation:

To solve the system of equations using the elimination method, we need to eliminate one variable. Multiplying the first equation by 2 will give us -8x + 2y = -12. Then, we can add the two equations together to eliminate the x variable.

-8x + 2y + (-8x - 2y) = -12 + 14

-16x = 2

x = -1/8

Substituting the value of x into the first equation:

-4(-1/8) + y = -6

1/2 + y = -6

y = -6 - 1/2

y = -12 - 1/2

y = -25/2

So, the solution to the system of equations is (x, y) = (-1/8, -25/2).