Solving Systems Using Substitution Chapter 7 Section 2 Solving Systems Using Substitution

Substitution allows you to create a one variable equation Steps Pick one equation and substitute its x or y value into the other equation Solve for the variable that is left Substitute the solution into the equation that you did not change and solve for the remaining variable Check to see if solution satisfies both equations

1 Examples Step 1 Step 2 Step 3 y = x + 6.1 Step 4 y = -2x – 1.4 x + 6.1 = -2x – 1.4 +2x +2x 3x + 6.1 = -1.4 –6.1 –6.1 3x = -7.5 3 3 x = -2.5 y = -2(-2.5) – 1.4 y = 5 – 1.4 y = 3.6 y = x + 6.1 y = -2x – 1.4 3.6=-2.5 + 6.1 3.6=-2(-2.5) – 1.4 3.6 = 3.6 3.6 = 5 – 1.4 3.6 = 3.6 The solution is (-2.5, 3.6)

2 1 car 3 vans 4 drivers and 22 students going on field trip – vans seat 6 - cars seat 4. How many cars and vans are needed for the trip? 6v + 4c = 22 6(-c + 4) + 4c = 22 -6c + 24 + 4c = 22 -2c + 24 = 22 – 24 – 24 -2c = -2 -2 -2 c = 1 v = # of vans c = # of cars v + c = 4 6v + 4c = 22 Solve by substitution 6v + 4(1) = 22 6v + 4 = 22 – 4 – 4 6v = 18 6 6 v = 3 v + c = 4 – c – c v = -c + 4 1 car 3 vans 4

3 No solution x + y = 6 5x + 5y = 10 5x + 5y = 10 5(-y + 6) + 5y = 10 30 = 10 Solve for x x + y = 6 – y – y x = -y + 6 No solution

infinite # of solutions To determine how many solutions a system has, refer to this chart of results 2 = 2 infinite # of solutions 10 ≠ 1 no solutions x = 4 one solution 6

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Assignments Class work Page 384 #1 – 4, 5 – 21 odd, 22 - 24 Page 385 #25 – 31 odd, 34 - 39 Homework Finish Class Work; Page 386 #46 – 48