Notes
Solving Systems of Equations by
Substitution
Review! - Solve each system of equation by graphing.
1)
2)
Solution:_______
Solution:_______
We are going to accomplish the exact same goal of finding the ordered pair,
__________, that satisfies BOTH equations, but use a more algebraic approach.
BIG IDEA: We will use our _____________ skills to isolate a variable in
whatever equation is the easiest. Then we will plug in that expression to the
OTHER equation, and solve for the remaining variable.
What will we do after that? We will ___________ the value we found to
one of the ________________ equations to solve for the other variable.
*If the letters disappear entirely, remember we can write _______________
solutions or _____ solution depending on what’s left!
Sounds complicated…let’s try it!
Example 1 : 3𝑥 + 2𝑦 = 8
𝑥 = 3𝑦 + 10
Example 2 : 3𝑥 − 4𝑦 = −15
5𝑥 + 𝑦 = −2
Solution: __________________________________
Solution: _________________________________
You try! - Solve each system of linear equations using substitution. Remember to
isolate whichever variable is the easiest and plug the expression into the OTHER
equation!
1) 𝑦 = −𝑥 + 6
𝑥 − 2𝑦 = −6
2) 𝑥 − 𝑦 = −15
𝑥 + 𝑦 = −5
Solution: __________________________________
Solution: _________________________________
3) 𝑥 = 3 − 3𝑦
4𝑦 = 𝑥 + 11
Solution: __________________________________
4) 𝑥 − 𝑦 = 1
2𝑥 + 𝑦 = 8
Solution: __________________________________