Question

name:____________________________ period.____
solving systems by the substitution method
example with mrs.razo:

equation #1	equation #2

step 1: in one of the equations, isolate one of the variables. this step may already be finished in many systems.
step 2: substitute the equivalent expression into the other equation for the proper variable.
step 3: solve to find either $x$ or $y$ (whichever was the variable you didnt substitute for).
step 4: plug your answer into one of the equations to find the other variable.
step 5: write your answer as a coordinate point, $(x,y)$.

Explanation:

Step1: Substitute \( y = x + 9 \) into \( 2x + 3y = 12 \)

We know \( y = x + 9 \), so replace \( y \) in \( 2x + 3y = 12 \) with \( x + 9 \). We get \( 2x + 3(x + 9)=12 \).

Step2: Simplify and solve for \( x \)

First, expand the left - hand side: \( 2x+3x + 27=12 \). Then combine like terms: \( 5x+27 = 12 \). Subtract 27 from both sides: \( 5x=12 - 27=- 15 \). Divide both sides by 5: \( x=\frac{-15}{5}=-3 \).

Step3: Find \( y \) by substituting \( x=-3 \) into \( y = x + 9 \)

Substitute \( x = - 3 \) into \( y=x + 9 \), we have \( y=-3 + 9 = 6 \).

Step4: Write the solution as a coordinate point

The solution of the system of equations is the ordered pair \((x,y)\) where \( x=-3 \) and \( y = 6 \).

Answer:

\((-3,6)\)