Question

problem 1
solve the following system
$5x - 7y = 58$
$y = -x + 2$
$x = \boxed{}$
$y = \boxed{}$
check

Explanation:

Step1: Substitute \( y = -x + 2 \) into \( 5x - 7y = 58 \)

Substitute \( y \) in the first equation: \( 5x - 7(-x + 2) = 58 \)

Step2: Simplify the equation

Expand the left - hand side: \( 5x + 7x-14 = 58 \)
Combine like terms: \( 12x-14 = 58 \)
Add 14 to both sides: \( 12x=58 + 14=72 \)

Step3: Solve for \( x \)

Divide both sides by 12: \( x=\frac{72}{12} = 6 \)

Step4: Solve for \( y \)

Substitute \( x = 6 \) into \( y=-x + 2 \): \( y=-6 + 2=-4 \)

Answer:

\( x = 6 \), \( y=-4 \)