Questions: Solve the system of equations. 12x-5y=-20 y=x+4 x= y=

Transcript text: Solve the system of equations. \[ \begin{array}{l} 12 x-5 y=-20 \\ y=x+4 \\ x=\square \\ y=\square \end{array} \]

Solution

Step 1: Substitute the Expression for \( y \) into the First Equation

Given the equation \( y = x + 4 \), substitute \( y \) in the first equation: \[ 12x - 5(x + 4) = -20 \]

Step 2: Simplify the Equation

Distribute and simplify the equation: \[ 12x - 5x - 20 = -20 \]

Step 3: Solve for \( x \)

Combine like terms: \[ 7x - 20 = -20 \] Add 20 to both sides: \[ 7x = 0 \] Divide by 7: \[ x = 0 \]

Step 4: Substitute \( x \) Back into the Expression for \( y \)

Substitute \( x = 0 \) into \( y = x + 4 \): \[ y = 0 + 4 \] \[ y = 4 \]

\[ x = \boxed{0}, \quad y = \boxed{4} \]

Was this solution helpful?

Unhelpful

Helpful

Thank you for your feedback.

Copied!