Question

solve the system of equations.
-4x + 7y = 20
y = 3x + 15
x =
y =

Explanation:

Step1: Substitute \( y = 3x + 15 \) into \( -4x + 7y = 20 \)

Substitute \( y \) in the first equation: \( -4x + 7(3x + 15) = 20 \)

Step2: Simplify and solve for \( x \)

Expand the equation: \( -4x + 21x + 105 = 20 \)
Combine like terms: \( 17x + 105 = 20 \)
Subtract 105 from both sides: \( 17x = 20 - 105 = -85 \)
Divide by 17: \( x = \frac{-85}{17} = -5 \)

Step3: Substitute \( x = -5 \) into \( y = 3x + 15 \)

Calculate \( y \): \( y = 3(-5) + 15 = -15 + 15 = 0 \)

Answer:

\( x = -5 \)
\( y = 0 \)