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## Solving Systems of Equations by Substitution

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**Solving Systems of Equations by Substitution**Objectives: Solve Systems of Equations using substitution. Solve Real World problems involving systems of equations.**Systems of Equations Review**• How many ways can two lines lie on a coordinate plane? • What is the solution for a system of equations in each case?**Substitution**• Solve each system of equations and state the solution(s) if solution(s) exist. Y = 5xand 2x +3y = 34 2x+3( ) = 34 2x + 15x = 34 17x = 34 17 x = 2 5x Y = 5( ) Y = 10 2 Solution =(2, 10)**Substitution**• Solve each system of equations and state the solution(s) if solution(s) exist. X + y = 16 and 2y = 2x + 2 y = 16 - x 2( ) = 2x + 2 32 – 2x = 2x + 2 32 = 4x + 2 30 = 4x 7.5 = x 16 - x**Substitution**• Solve each system of equations and state the solution(s) if solution(s) exist. X + 3y = 12 and x – y = 8**Substitution**• Solve each system of equations and state the solution(s) if solution(s) exist. Y= 3/5 x and 3x – 5y = 15**Substitution**• Solve each system of equations and state the solution(s) if solution(s) exist. Y=3x+2 and 6x -2y = -4**Substitution**• C – 5d = 2 and 2c + d = 4**Substitution**• 5r – s = 5 and -4r + 5s = 17**Assignment**• Page 379 #11-17 • SHOW WORK!!! • Remember Solution is an ordered pair.