System by Elimination Adding and Subtracting

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

• Substitution

• Elimination

What is the purpose of multiplying the equations in the elimination method?

• To waste time and effort

• To confuse the person solving the equations

• To make the equations look more complicated

• To create opposite coefficients for one of the variables

What variable do you eliminate?

4x + 8y = 20

−4x + 2y = −30

• X because they have opposite signs

• Y because they have opposite signs

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

Solve the system of equations.

Use scrap paper/dry erase to work this out

      x + 5y = -27

-2x - 5y = 24

• (3, 6)

• (-3, -6)

• (-3, -4)

• (3, -6)

Solve the system by elimination.  

−8x − 10y = 20
−8x − 6y = −4 

• Infinite number of solutions  

• (6, 5) 

• (−6, −5) 

• (5, −6) 

Solve the system of Equation (x,y)
3x + 2y = –13
3x + 4y = 1 

• (-9,7)

• (7,-9)

• (4,-7)

• (-7,-4)

Given the problem:
y = 3x + 1
y = 5x - 9
Step 1: 3x + 1 = 5x - 9
Step 2: -2x + 1 = 9
Step 3: What is the next step?

• Add 1 to both sides

• Subtract 1 from both sides

• Add 2x to both sides

• Add 9 to both sides

eliminate one of the variables in a system of equations by adding or subtracting the equations

• elimination method

• substitution method

• linear programming