Questions: Use substitution to solve the system. 2x+9=y 5x-3y=-23 x= y=

Transcript text: Use substitution to solve the system. \[ \begin{array}{c} 2 x+9=y \\ 5 x-3 y=-23 \end{array} \] \[ \begin{array}{l} x= \\ y= \end{array} \]

Solution

Solution Steps

To solve the system of equations using substitution, we first solve the first equation for \( y \) in terms of \( x \). Then, substitute this expression for \( y \) into the second equation to solve for \( x \). Once \( x \) is found, substitute it back into the expression for \( y \) to find the value of \( y \).

Step 1: Solve for \( y \)

From the first equation \( 2x + 9 = y \), we can express \( y \) in terms of \( x \): \[ y = 2x + 9 \]

Step 2: Substitute \( y \) into the second equation

Next, we substitute \( y \) into the second equation \( 5x - 3y = -23 \): \[ 5x - 3(2x + 9) = -23 \]

Step 3: Solve for \( x \)

Expanding and simplifying the equation: \[ 5x - 6x - 27 = -23 \] \[ -x - 27 = -23 \] Adding 27 to both sides: \[ -x = 4 \] Thus, we find: \[ x = -4 \]

Step 4: Substitute \( x \) back to find \( y \)

Now, we substitute \( x = -4 \) back into the expression for \( y \): \[ y = 2(-4) + 9 = -8 + 9 = 1 \]