Lesson 2.8 Solving system of equations by substitution

1. Lesson 2.8Solving system of equations by substitution ‘In Common’ Ballad: http://youtu.be/Br7qn4yLf-I ‘All I do is solve’ Rap: http://youtu.be/1qHTmxlaZWQ

2. Key concepts • There are various methods to solving a system of equations. A few days ago we looked at the graphing method. Today we are going to look at the substitution method. • The substitution method involves solving one of the equations for one of the variables and substituting that into the other equation. • Solutions to systems are written as an ordered pair, (x,y). This is where the lines would cross if graphed.

3. Key concepts continued • If the resulting solution is a true statement, such as 9 = 9, then the system has an infinite number of solutions. This is where the lines would coincide if graphed. • If the result is an untrue statement, such as 4 = 9, then the system has no solutions. This is where lines would be parallel if graphed. • Check your answer by substituting the x and y values back into the original equations. If the answer is correct, the equations will result in true statements.

4. Steps for substitution method • Step 1: Solve one of the equations for one of its variables. • Step 2: Substitute the expression from step 1 into the other equation. • Step 3: Solve the equation from step 2 for the other variable. • Step 4: Substitute the value from step 3 into the revised equation from step 1 (or either of the original equations) and solve for the other variable.

5. Example 1: • Step 1: Solve one of the equations for one of its variables. • It doesn’t matter which equation you choose, nor does it matter which variable you solve for. • Let’s solve for the variable y. Isolate y by subtracting x from both sides.

6. Step 2: Substitute into the other equation, . • It helps to place parentheses around the expression you are substituting. • Step 3: Solve the equation from step 2 for the other variable. Second equation of the system. Substitute for y. Distribute the negative over Simplify. Add 2 to both sides. Divide both sides by 2.

7. Step 4: Substitute the value, (), into the revised equation from step 1 (or either of the original equations) and solve for the other variable. • The solution to the system of equations is (). If graphed, the lines would cross at (). Revised equation from step 1. Substitute for . Simplify.

8. Example 2: • Step 1: Solve one of the equations for one of its variables. • It doesn’t matter which equation you choose, nor does it matter which variable you solve for. • Let’s solve for the variable x. Isolate by adding to both sides.

9. Step 2: Substitute into the other equation, . • It helps to place parentheses around the expression you are substituting. • Step 3: Solve the equation from step 2 for the other variable. Second equation of the system. Substitute for . Distribute the 4 through Simplify. Add 12 to both sides. Divide both sides by 5.

10. Revised equation from step 1. • Step 4: Substitute the value, (), into the revised equation from step 1 (or either of the original equations) and solve for the other variable. • The solution to the system of equations is (). If graphed, the lines would cross at (). Substitute for y. Simplify.

11. You try! 1) 2)