Solving Systems of Equations Algebraically

Solving Systems of Equations Algebraically

Chapter 3 - Lesson 8

Page 244 to 249

What is SUBSTITUTION?

• to replace a variable with a number (or an expression).

example 1: solve the follwing equation   $y=5x$  , if  $x=2$  

Example 2: The perimeter (P) of a square equals the length of one side times 4. Find the perimeter of a triangle if one side is 30 meters.

Using SUBSTITUTION to Solve Systems of Equations

•  $y=2x-8$  

•  $y=2$  

What does the solution to the system of equations mean?

• y=2x-8

• y=2

• if we graph the lines, they intesect at one point.

Using SUBSTITUTION to Solve Systems of Equations

•  $y=x-3$  

•  $y=2x$  

Comparing the solution with the graphs of the lines

• y=x-3

• y=2x

• Where do the two lines intesect?

Multiple Choice

Solve the system of equations algebraically

 $y=x+7$  
 $y=4$  

• (-3,4)

• (4,-3)

• (3,-4)

• (-3,4)

Multiple Choice

Solve the system of equations algebraically

 $y=x+6$  
 $y=3x$  

• (3,9)

• (-3,9)

• (3,-9)

• (-3,-9)

Multiple Choice

Solve the system of equation algebraically

 $y=2x-5$  
 $y=x+2$  

• (7,9)

• (-7,9)

• (7,-9)

• (-7,-9)

Solve the following algebraically, then graph the lines on DESMOS to see what the lines look like and what type of solutions they have.

Multiple Choice

Solve the system of equation algebraically

 $y=5x+2$  
 $y=5x-2$  

• No solution

• Infinite Solutions

• (5,-2)

• (5,2)

Multiple Choice

Solve the systems of equations algebraically
 $y=-3x+2$  

 $y+3x=2$  

• Infinite Solutions

• No Solutions

• (-3,2)

• (3,2)

Types of solutions to a System of Equations

• One solution: different slope

• No solution: same slope, different y-intercept

• Infinite Solutions: same slope, same y-intercept