Question

for this assignment.
solve the system by substitution.
$2x - 3y = 38$
$-x - 6 = y$

Explanation:

Step1: Substitute \( y = -x - 6 \) into the first equation

We have the first equation \( 2x - 3y = 38 \) and \( y = -x - 6 \). Substitute \( y \) in the first equation:
\( 2x - 3(-x - 6) = 38 \)

Step2: Simplify the equation

Expand the left - hand side: \( 2x+3x + 18=38 \)
Combine like terms: \( 5x+18 = 38 \)
Subtract 18 from both sides: \( 5x=38 - 18=20 \)

Step3: Solve for \( x \)

Divide both sides by 5: \( x=\frac{20}{5} = 4 \)

Step4: Solve for \( y \)

Substitute \( x = 4 \) into \( y=-x - 6 \): \( y=-4 - 6=-10 \)

Answer:

The solution of the system is \( x = 4,y=-10 \)