Question

solve by the elimination method.
8x + 5y = -31
-8x + y = 61
what is the solution of the system? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. (square) (type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Add the two equations

We have the system:

$$
LATEXBLOCK0
$$

Adding the two equations together to eliminate \(x\):
\((8x + 5y)+(-8x + y)=-31 + 61\)
Simplify the left side: \(8x-8x + 5y + y=6y\)
Simplify the right side: \(30\)
So we get \(6y = 30\)

Step2: Solve for y

Divide both sides of \(6y = 30\) by 6:
\(y=\frac{30}{6}=5\)

Step3: Substitute y into one equation

Substitute \(y = 5\) into the second equation \(-8x + y=61\):
\(-8x+5 = 61\)
Subtract 5 from both sides:
\(-8x=61 - 5=56\)
Divide both sides by \(-8\):
\(x=\frac{56}{-8}=-7\)

Answer:

\((-7, 5)\)