Questions: Find the solution to the system of equations by substitution. x+9y=9 5x-7y=-7 (0,0) (1,1) (1,0) (0,1)

Transcript text: Find the solution to the system of equations by substitution. \[ \begin{array}{l} x+9 y=9 \\ 5 x-7 y=-7 \end{array} \] $(0,0)$ $(1,1)$ $(1,0)$ $(0,1)$

Solution

Solution Steps

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

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

Step 1: Solve the First Equation for $ x $

Given the first equation: \[ x + 9y = 9 \] We solve for $ x $: \[ x = 9 - 9y \]

Step 2: Substitute $ x $ into the Second Equation

Substitute $ x = 9 - 9y $ into the second equation: \[ 5x - 7y = -7 \] \[ 5(9 - 9y) - 7y = -7 \] \[ 45 - 45y - 7y = -7 \] \[ 45 - 52y = -7 \]

Step 3: Solve for $ y $

Solve the equation: \[ 45 - 52y = -7 \] \[ -52y = -7 - 45 \] \[ -52y = -52 \] \[ y = 1 \]

Step 4: Substitute $ y $ back into the Expression for $ x $

Substitute $ y = 1 $ back into $ x = 9 - 9y $: \[ x = 9 - 9(1) \] \[ x = 0 \]