Lesson 2.8 Solving system of equations by substitution

1 / 11

# Lesson 2.8 Solving system of equations by substitution - PowerPoint PPT Presentation

Lesson 2.8 Solving 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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Lesson 2.8 Solving system of equations by substitution' - hetal

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Lesson 2.8Solving system of equations by substitution

‘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.

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.