Question

solve the following system of equations.
8x + 9y = -1
-2x + 3y = -5
x =

y =

Explanation:

Step1: Eliminate x by multiplying the second equation

Multiply the second equation \(-2x + 3y = -5\) by 4 to get \(-8x + 12y = -20\).

Step2: Add the two equations

Add the first equation \(8x + 9y = -1\) and the new second equation \(-8x + 12y = -20\):
$$(8x - 8x) + (9y + 12y) = -1 + (-20)$$
$$21y = -21$$

Step3: Solve for y

Divide both sides by 21: \(y = \frac{-21}{21} = -1\).

Step4: Substitute y into the second equation

Substitute \(y = -1\) into \(-2x + 3y = -5\):
$$-2x + 3(-1) = -5$$
$$-2x - 3 = -5$$

Step5: Solve for x

Add 3 to both sides: \(-2x = -5 + 3 = -2\), then divide by -2: \(x = \frac{-2}{-2} = 1\).

Answer:

\(x = 1\)
\(y = -1\)