Question

1. $2x + 3y = 13$

$7x + 8y = -32$

Explanation:

Step1: Eliminate one variable (e.g., x)

Multiply the first equation \(2x + 3y = 13\) by 7: \(14x + 21y = 91\)
Multiply the second equation \(7x + 8y = -32\) by 2: \(14x + 16y = -64\)

Step2: Subtract the two new equations

\((14x + 21y) - (14x + 16y) = 91 - (-64)\)
Simplify: \(5y = 155\)

Step3: Solve for y

\(y = \frac{155}{5} = 31\)

Step4: Substitute y = 31 into first equation

\(2x + 3(31) = 13\)
\(2x + 93 = 13\)
\(2x = 13 - 93 = -80\)
\(x = \frac{-80}{2} = -40\)

Answer:

\(x = -40\), \(y = 31\)