1. 30S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solving Systems of Equations Algebraically Find x 3(x - 2) = 2x + 3(x + 5) - 1 Learning Outcome B-1 SLE-L2 Objectives: Solve systems of equations using algebraic methods

2. 30S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Solving Systems Algebraically Lesson: SLE-L2 A system of linear equations can be solved algebraically. It may be more convenient and more efficient to solve the system using technology, but an algebraic method gives an exact solution. The algebraic method first eliminates one variable, and the resulting equation, with one variable, is solved using simple methods. Theory – Solving an Equation

3. 30S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Solving Systems Algebraically Lesson: SLE-L2 The Substitution Method uses the following procedure: 1.Solve one of the equations for one variable (whichever is more convenient). 2.Substitute that value into the other equation. 3.Solve for the other variable. 4.Substitute the resulting value into either original equation to find the value of the second variable. 5.Check the solution in both original equations. Theory – Substitution Method

4. 30S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Substitution Method. 3x + 4y = -2 2x – y = 17 Theory – Substitution Method

5. 30S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Substitution Method. 2x - y = 5 -x + y = -3 Theory – Substitution Method

6. 30S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Substitution Method. 4x - 3y = 2 2x + y = -4 Theory – Substitution Method

7. 30S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Solving Systems Algebraically Lesson: SLE-L2 The Addition Subtraction Method uses the following procedure: 1.(If necessary) Multiply one equation (or both) by a scalar factor(s) to create common-magnitude coefficients on one variable. 2.Add or subtract the equations to make this variable disappear from the resultant equation. 3.Solve your new one-variable equation. 4.Substitute the resulting value into either original equation to find the value of the second variable. 5.Check the solution in both original equations. Theory – Addition Subtraction Method

8. 30S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Addition Subtraction Method. 2x + 3y = 9 -2x - 5y = 1 Theory – Addition Subtraction Method

9. 30S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Solving Systems Algebraically Lesson: SLE-L2 What to Do When the Coefficients Are Not Alike. Example: 2x+3y=1 (Equation 1) 5x-4y=14 (Equation 2) Solve & check. Theory – Addition Subtraction Method

10. 30S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Addition Subtraction Method. 3x - 2y = 10 5x - 3y = -15 Theory – Addition Subtraction Method

11. 30S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Addition Subtraction Method. 3y - x = 1 6y – 2x = 5 Theory – Addition Subtraction Method

12. 30S Applied Math Mr. Knight – Killarney School Slide 12 Unit: Solving Systems Algebraically Lesson: SLE-L2 Solve the following system using the Addition Subtraction Method. 3y - x = 1 6y – 2x = 2 Theory – Addition Subtraction Method