Systems of Equations Using the Elimination Method

Use the Elimination method to solve the system.

-7x - 5y = 12

7x + 5y = -12

• (0, 0)

• (1, 1)

• Infinitely Many Solutions

• No Solution

7x - y = 10

-7x + y = -14

• No Solution

• (4, 1)

• Infinitely Many Solutions

• (2, -4)

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Identify which method for solving systems is being described by this fact: Equations must have like terms "stacked" up vertically, usually written in standard form.

• Graphing

• Substitution

• Elimination (linear combination)

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Solve for x and solve for y
3x  - 3y = 33
6x - 3y = 57

• (8,-3)

• (-3,8)

• (10,1)

• (10,-1)

When solving the system, if you get a result of something like 6 = 6 or -2 = -2 and the answer is:

• No Solution

• Infinitely Many Solutions

• Not possible

Which is the best method for solving this system of equations?

-4x-2y=-12

4x+8y=-24

• Substitution

• Elimination

• Graphing, Not Graphing...

  (aka Picturing the Graph)

  (aka Using graphing skills but not actually graphing)

Should you use the Substitution or Elimination method to solve this system of equations?

• Substitution

• Elimination