Question

#8 -2x + 9y = -13 -5x + 3y = 26

Explanation:

Step1: Eliminate \( y \) by multiplying the second equation

Multiply the second equation \(-5x + 3y = 26\) by \( 3 \) to make the coefficients of \( y \) in both equations have a common multiple.
\( 3\times(-5x + 3y)=3\times26 \)
\( -15x + 9y = 78 \)

Step2: Subtract the first equation from the new equation

Subtract the first equation \(-2x + 9y = -13\) from \(-15x + 9y = 78\).
\((-15x + 9y)-(-2x + 9y)=78 - (-13)\)
\(-15x + 9y + 2x - 9y = 78 + 13\)
\(-13x = 91\)

Step3: Solve for \( x \)

Divide both sides of \(-13x = 91\) by \(-13\).
\( x=\frac{91}{-13}=-7 \)

Step4: Substitute \( x = -7 \) into the first equation to solve for \( y \)

Substitute \( x = -7 \) into \(-2x + 9y = -13\).
\(-2\times(-7)+9y=-13\)
\( 14 + 9y = -13 \)
Subtract \( 14 \) from both sides: \( 9y=-13 - 14=-27 \)
Divide both sides by \( 9 \): \( y=\frac{-27}{9}=-3 \)

Answer:

\( x = -7 \), \( y = -3 \)