1. Solving Systems Algebraically
Skill 42

2. Objective
HSA-REI.5: Prove that given two equations replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Solve systems of equations algebraically.

3. Example; Solve the System
𝑦=2𝑥+3 𝑥+𝑦=−3
𝑥+ 𝟐𝒙+𝟑 =−3
𝑦=2𝑥+3
3𝑥+3=−3
𝑦=2 −2 +3
3𝑥=−6
𝑦=−4+3
𝑥=−2
𝑦=−1
(-2, -1)

4. Example; Solve the System
𝑦=−2𝑥+1 2𝑥+3𝑦=19
2𝑥+3 −𝟐𝒙+𝟏 =19
𝑦=−2𝑥+1
2𝑥−6𝑥+3=19
𝑦=−2 −4 +1
𝑦=8+1
−4𝑥+3=19
−4𝑥=16
𝑦=9
𝑥=−4
(-4, 9)

5. Example; Solve the System
(5)
−3𝑥+4𝑦=−15 5𝑥+2𝑦=−1
(3)
5𝑥+2𝑦=−1
−15𝑥+20𝑦=−75 15𝑥+6𝑦=−3
5𝑥+2 −3 =−1 +
5𝑥−6=−1
26𝑦=−78
5𝑥=5
𝑦=−3
𝑥=1
(1, -3)

6. Example; Solve the System
(-2)
7𝑥−3𝑦=−1 8𝑥−6𝑦=4
(1)
8𝑥−6𝑦=4
−14𝑥+6𝑦=2 8𝑥−6𝑦=4
8 −1 −6𝑦=4 +
−8−6𝑦=4
−6𝑥=12
−6𝑥=6
𝑥=−1
𝑦=−2
(-1, -2)

7. #42: Solving Systems Algebraically
Questions
Summarize Notes
Homework
Google Classroom
Quiz