Question

Solve the system of equations using elimination:

-9x - 8y = 11
-4x - 8y = -4

a) x = -1, y = 1
b) x = 2, y = -3
c) x = -3, y = 2
d) x = 1, y = -1

Answer 1

By subtracting the second equation from the first in the given system and then solving for x, we find x = -3. Substituting this value back into one of the original equations, we determine that y = 2. Hence, the correct answer is c) x = -3, y = 2.

The correct option is c.

Step-by-step explanation:

To solve the system of equations using elimination, we first look at the two given equations:

-9x - 8y = 11

-4x - 8y = -4

We want to eliminate one of the variables. In this case, subtracting the second equation from the first gives us:

-9x - 8y - (-4x - 8y) = 11 - (-4)

This simplifies to:

-5x = 15

Dividing both sides by -5 yields:

x = -3

Now, substitute x = -3 back into either original equation to solve for y:

-9(-3) - 8y = 11

27 - 8y = 11

Subtract 27 from both sides:

-8y = -16

Divide by -8:

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2, which corresponds to letter c) x = -3, y = 2.

The correct option is c.