Solving Systems Algebraically Skill 42

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.

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)

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)

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)

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)

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