1. Solving a System of Equations in Two Variables By Substitution Chapter 8.2

2. Steps to solve a system of equations using the substitution method 1.Take one equation and solve for one variable. 2.Substitute this expression into that variable in the other equation. 3.You now have an equation with one variable. Solve to find the value of this variable. 4.Substitute this value into the equation made in step 1. 5.Check the solution.

3. 1. Find the solution. 5x + 3 -2x -2x 2x – -y = -2x + 12 y = -1 -1 -1 step 1 solve for y y = 12 2x y= 19 – 12

4. 1. Find the solution. -2x 2x – -y = -2x + 12 y = -1 -1 -1 step 2 substitute into y y = 12 2x – 12 5x + 3 y= 19 5x + 3 (2x – 12)= 19

5. 1. Find the solution. -2x 2x – -y = -2x + 12 y = -1 -1 -1 step 3 solve for x y = 12 2x – 12 5x + 3 y= 19 5x + 3 (2x – 12)= 19 5x + 6x= 19 – 36 11x= 19 – 36 +36 +36 11x = 55 11 11 x = 5

6. 1. Find the solution. -2x 2x – -y = -2x + 12 y = -1 -1 -1 step 4 substitute and solve for y y = 12 2x – 12 5x + 3 y= 19 5x + 3 (2x – 12)= 19 5x + 6x= 19 – 36 11x= 19 – 36 +36 11x = 55 11 x = 5 y = 2(5) – 12 y = 10 – 12 y = - 2 (5, - 2)

7. 5(5) + 3( - 2) = 19 25 √ 2(5) – ( - 2) = 12 10 √ 1. Find the solution. 2x – step 5 check y = 12 5x + 3 y= 19 (5, - 2) – 6 = 19 + 2= 12

8. x  x –  y = 1 Before beginning change the first equation by multiplying each term by the LCD. 2. Find the solution. 6(  x) – 6(  y) = 6(1) 2 – 3y = 6 Now solve with these equations. However when we check we will use the original equations. x + 4y = - 8

9. 2. Find the solution. -4y -4y x = step 1 solve for x -4y – 8 x 2 – 3y = 6 x + 4y = - 8

10. 2. Find the solution. -4y x = step 2 substitute into x -4y – 8 x 2 – 3y = 6 x + 4y = - 8 2 – 3y= 6 (-4y – 8)

11. 2. Find the solution. -4y x = step 3 solve for y -4y – 8 x 2 – 3y = 6 x + 4y = - 8 2(-4y – 8) – 3y= 6 -8y – 3y= 6– 16 -11y = 6– 16 +16 +16 -11y = 22 -11 -11 y = - 2

12. 2. Find the solution. -4y x = step 4 substitute and solve for x -4y – 8 x 2 – 3y = 6 x + 4y = - 8 2(-4y – 8) – 3y= 6 -8y – 3y= 6– 16 -11y = 6– 16 +16 -11y = 22 -11 y = - 2 x = -4( - 2) – 8 x = 8 – 8 x = 0 (0, - 2)

13. 2. Find the solution. step 5 check with the original equations x + 4y = - 8 (0, - 2)  x –  y = 1  (0) –  ( - 2) = 1 0 √ (0) + 4( - 2) = - 8 √ + 1 = 1 - 8= - 8

14. Solving a System of Equations in Two Variables By Substitution Chapter 8.2