Lesson 3 – Solving Linear Systems by Substitution
WARMUP
Solve the linear system by graphing.
3𝑦 + 𝑥 = 12
𝑦 = 2𝑥 − 1
Why is graphing not an accurate way to solve a linear system?
We need a better method. SUBSTITUTION AND ELIMINATION TO THE RESCUE!!
SOLVING LINEAR SYSTEMS BY SUBSTITUTION
Example ①
2𝑥 − 3𝑦 = −2
Label the equations 1 and 2
4𝑥 + 𝑦 = 24
Step 1: Isolate the variable in one of the equations (look for the variable that has a coefficient of 1)
Step 2: Substitute the equivalent equation from step 1 into the other equation
Step 3: Substitute this value into either equation 1 or 2 to determine the value of the other variable
Step 4: Check by substituting into both original equations
Step 5: State the solution
Example ②
5𝑎 + 𝑏 = 4
3𝑎 + 2𝑏 = −6
Example ③
2𝑚 − 3𝑛 = −10
4𝑚 + 𝑛 = 1