6. Elimination Method.pptx MATHEMATICS 8

MATH 8

1. System of Linear Equations or Simultaneous Equations Grade 8

2. Learning Outcomes Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs Solve systems of two linear equations in two variables algebraically

3. System of Linear Equations Simultaneous equations are two or more algebraic equations that can be solved at the same time. Linear simultaneous equations with two unknown variables can be solved by using the following methods: Graphical Method Elimination Method Substitution Method

4. Graphs of Simultaneous Equations 1 2 3 4 -4 -3 -2 -1 1 2 3 4 The solutions of simultaneous equations with two unknown variables correspond to the point of intersection of their graphs. -4 -3 -2 -1 Here is a system of two equations: x + y = 2 y = x + 1 The solution to the simultaneous equations is x = 0.5, y = 1.5 x + y = 2 y = x + 1

5. Elimination Method In the elimination method, one variable is eliminated by adding or subtracting the equations. This leaves one equation with one variable. x + 4y = 6 x + 3y = 4 - y = 2 Subtracting these equations eliminates the x variable x + 2y = 6 3x - 2y = 10 + 4x = 16 Adding these equations eliminates the y variable

6. Example 1 5x + 2y = 24 3x + 2y = 16 - 2x x = 4 1 2 Substitute into equation 5(4) + 2y = 24 20 + 2y = 24 2y = 4 y = 2 Solve the equation for y Look for the same coefficient. Subtract if they both have the same sign 1 x = 4, y = 2 The y variable has been eliminated, solve for x = 8 2 2 5x + 2y = 24

7. Example 2 2x - 2y = - 6 x + 2y = 3 + 3x = - 3 x = - 1 1 2 Substitute into equation 2(-1) - 2y = - 6 -2 - 2y = - 6 - 2y = - 4 y = 2 Solve the equation for y Look for the same coefficient. Add if they have different signs 1 x = -1, y = 2 The y variable has been eliminated, solve for x

8. More Examples: 3 3x + 2y = 11 3x + y = 7 y = 4 Substitute y = 4 3x + 2y = 11 3x + 2(4) = 11 3x + 8 = 11 3x = 11 – 8 3x = 3 3 3 x = 1

9. More Examples: 4 3x + 2y = 12 x + 2y = 8 2x = 4 2 2 x = 2 Substitute x = 2 3x + 2y = 12 3(2) + 2y = 12 6 + 2y = 12 2y = 12 – 6 2y = 6 y = 3

10. More Examples: 5 3x - y = 10 2x + y = 5 + 5x = 15 5 5 x = 3 Substitute x = 3 3x - y = 10 3(3) - y = 10 9 - y = 10 - y = 10 – 9 - y = 1 y = -1

11. DRILL

12. First 10 1 2 3 4 2x + 3y = 8 2x - 3y = 0 3x - 2y = 5 3x + 5y = -2 3x + y = 2 x + 2y = 4 x + 2y = 8 3x - 2y = 8 5 2x - 5y = 17 6x - 5y = 1

13. WRITTEN WORK 1 2 3 4 a – 3b = 4 2a + 3b = 5 7x + y = 42 -3x + y = -8 x + y = 7 3x + 2y = 17 2m - n = 3 m + n = 9 5 x - 3y = 13 x + 2y = 5