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Lesson 2.8 Solving system of equations by substitution PowerPoint Presentation

Lesson 2.8 Solving system of equations by substitution

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### 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

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.

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.

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.

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.

- 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.

- 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.

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.

- 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.

- 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.

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