Question

5x - 7y = 9\
9x + 5y = -19\
x = \square\
y = \square

Explanation:

Step1: Eliminate \( y \) by multiplying equations

Multiply the first equation \( 5x - 7y = 9 \) by \( 5 \): \( 25x - 35y = 45 \).
Multiply the second equation \( 9x + 5y = -19 \) by \( 7 \): \( 63x + 35y = -133 \).

Step2: Add the two new equations

Add \( 25x - 35y = 45 \) and \( 63x + 35y = -133 \):
\( (25x + 63x) + (-35y + 35y) = 45 + (-133) \)
\( 88x = -88 \)

Step3: Solve for \( x \)

Divide both sides by \( 88 \): \( x = \frac{-88}{88} = -1 \).

Step4: Substitute \( x = -1 \) into first equation

Substitute \( x = -1 \) into \( 5x - 7y = 9 \):
\( 5(-1) - 7y = 9 \)
\( -5 - 7y = 9 \)

Step5: Solve for \( y \)

Add \( 5 \) to both sides: \( -7y = 14 \).
Divide by \( -7 \): \( y = \frac{14}{-7} = -2 \).

Answer:

\( x = -1 \), \( y = -2 \)