Question

solve the system by substitution.
$4x - 6 = y$
$x - y = -9$

Explanation:

Step1: Substitute \( y = 4x - 6 \) into \( x - y = -9 \)

We know from the first equation that \( y = 4x - 6 \). Substitute this expression for \( y \) into the second equation \( x - y = -9 \). So we get \( x - (4x - 6) = -9 \).

Step2: Simplify the equation

Simplify \( x - (4x - 6) = -9 \). First, distribute the negative sign: \( x - 4x + 6 = -9 \). Then combine like terms: \( -3x + 6 = -9 \).

Step3: Solve for \( x \)

Subtract 6 from both sides: \( -3x = -9 - 6 \), which simplifies to \( -3x = -15 \). Then divide both sides by -3: \( x = \frac{-15}{-3} = 5 \).

Step4: Solve for \( y \)

Substitute \( x = 5 \) into the first equation \( y = 4x - 6 \). So \( y = 4(5) - 6 = 20 - 6 = 14 \).

Answer:

The solution to the system is \( x = 5 \) and \( y = 14 \).