Solving Systems by Elimination- Day 2

Solving Systems by Elimination

LET'S EXPLORE!

Solving Linear Systems by Elimination

Sometimes we can add equations that have two variables to obtain a new equation that only has one variable. In this sense, we are ELIMINATING a variable in order to solve the system

Steps:

Add or subtract the equations to eliminate one variable Solve the new equation Substitute value found in step 2 into either original equation to find the value of the other variable

Example 1 ....

Solve the linear system by adding the equations

2x + 3y = 11

-2x + 5y = 13

Example 2 ...

Solve the linear system by adding the equations

4x + 3y = 2

5x - 3y = -2

Example 3 ...

Solve the linear system by adding the equations

8x - 4y = -4

3x + 4y =15

​https://www.youtube.com/watch?v=dhqqoakuuAI

​https://www.youtube.com/watch?v=dhqqoakuuAI

You try....

Solve the linear system of equations. Remember to write your answer as an ordered pair (x,y)

-5x - 6y = 8

5x + 2y = 4

You try....

Solve the linear system of equations. Remember to write your answer as an ordered pair (x,y)

4x - 3y = 5

-2x + 3y = -7

Multiple Choice

When you solve the system of equations, what is the solution for x?

• 4

• -1

• -4

• 1

Multiple Choice

When you solve the system of equations, what is the solution for y?

• 8

• -1

• 1

• -8

Multiple Choice

Which variable would be easiest to eliminate?

• x

• y

• Neither

Multiple Choice

To eliminate a variable in the system, should you add the equations or subtract the equations?

• Add

• Subtract

• Neither

Multiple Choice

• (-3, 2)

• (3, 2)

• (-2, 3)

• (2, -3)

Multiple Choice

• (-7, -1)

• (1, 7)

• (-1, -7)

• (7, 1)

Multiple Choice

• (4, -2)

• (-2, 4)

• (2, 4)

• (2, -4)

Multiple Choice

Given the system of equations, what is the value of x + y?

• 2

• 8

• 6

• 0

Multiple Choice

• (-5, -9)

• (9, 5)

• (5, 9)

• (-9, -5)

Multiple Choice

• (4, -2)

• (-2, 4)

• (2, 4)

• (2, -4)

Multiple Choice

Solve the system of equations.

x + 5y = -27

2x + 5y = -24

• (3, 6)

• (-3, -6)

• (-3, -4)

• (3, -6)

Multiple Choice

Solve the following using elimination.
7x-9y=29
7x+2y=-15

• (-4,-1)
• (-1.-4)
• (-1,4)
• (-1,6)

Multiple Choice

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x
• The  y
• The  z
• The unknown

Multiple Choice

Solve by elimination:

7x-9y=29

7x+2y=-15

• (-4,-1)

• (-1,-4)

• (-1,4)

• (-1,6)

Multiple Choice

• (1, 4)

• (4, 1)

• (1, -4)

• (-4, 1)

Multiple Choice

Solve using elimination.

-2x+2y=0

2x+6y=-16

• (-2,-9)

• (-2,-2)

• no solution

• infinitely many solutions

Multiple Choice

Solve using elimination.

-6x-6y=18

6x+6y=-24

• (7,8)

• (-7,-8)

• no solution

• infinitely many solutions

Multiple Choice

Solve using elimination.

4x-2y=16

5x+2y=11

• (3,-2)

• (1,4)

• no solution

• infinitely many solutions

Multiple Choice

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)

Multiple Choice

$$3x-2y=12$$  

$$2x+2y=-2$$   What variable will eliminate in the system? 

• x

• y

• both

• neither

Multiple Choice

4x + 8y = 20

-4x + 2y = -30

Which variable will be eliminated?

• The x

• The y

• The unknown

Multiple Choice

Solve by elimination:

7x+y=-9

-3x-y=5

• No solution

• (-1,8)

• (-2,-3)

• (-1,-2)