Question

solve the system of equations.
$-5x + 4y = 3$
$x = 2y - 15$
$x = \boxed{2y}$
$y = \boxed{-5}$
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systems of equations with substitution: $-3x - 4y = -2$ & $y = 2x - 5$
4 of 4

Explanation:

Step1: Substitute \( x = 2y - 15 \) into \( -5x + 4y = 3 \)

Substitute \( x \) in the first equation: \( -5(2y - 15) + 4y = 3 \)

Step2: Expand and simplify the equation

Expand: \( -10y + 75 + 4y = 3 \)
Combine like terms: \( -6y + 75 = 3 \)
Subtract 75 from both sides: \( -6y = 3 - 75 = -72 \)
Divide by -6: \( y = \frac{-72}{-6} = 12 \)

Step3: Find \( x \) using \( x = 2y - 15 \)

Substitute \( y = 12 \): \( x = 2(12) - 15 = 24 - 15 = 9 \)

Answer:

\( x = 9 \), \( y = 12 \)