Questions: Use substitution -5x + 2y = 13 y = 2x + 6 x= y=

Transcript text: Use substitution \[ \begin{aligned} -5 x+2 y & =13 \\ y & =2 x+6 \end{aligned} \] \[ \begin{array}{l} x= \\ y= \end{array} \] $\square$ $\square$

Solution

Solution Steps

To solve the system of equations using substitution, we can follow these steps:

Substitute the expression for $ y $ from the second equation into the first equation.
Solve the resulting equation for $ x $.
Substitute the value of $ x $ back into the second equation to find $ y $.

Step 1: Substitute $ y $ from the second equation into the first equation

Given the system of equations: \[ \begin{aligned} -5x + 2y &= 13 \\ y &= 2x + 6 \end{aligned} \] Substitute $ y = 2x + 6 $ into the first equation: \[ -5x + 2(2x + 6) = 13 \]

Step 2: Simplify and solve for $ x $

Simplify the equation: \[ -5x + 4x + 12 = 13 \] Combine like terms: \[ -x + 12 = 13 \] Solve for $ x $: \[ -x = 1 \implies x = -1 \]

Step 3: Substitute $ x $ back into the second equation to find $ y $

Substitute $ x = -1 $ into $ y = 2x + 6 $: \[ y = 2(-1) + 6 = 4 \]