Elimination Method Add and Subtract

What is the first step in solving a system of equations by elimination?

• Rewrite the equations so the variables are all on the same side and line up the like terms.

• Get both equations in slope-intercept form.

• Get both equations equal to zero.

• Put the x terms first.

Answer explanation

We need all of the variables on the same side so that we can eventually add the left side of both equations together and add the right side of both equations together.

If the variables aren't on the same side of the equal-sign, then we can't combine like terms.

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

• Add

• Subtract

• Neither

Answer explanation

We want to add the equations together in order to eliminate one of the variables. We have opposite terms (3x and -3x) that will "cancel/zero out" (be eliminated) when we add the equations together.

Which variable would be easiest to eliminate?

• x

• y

• Neither

Answer explanation

The terms with x in them have opposite coefficients (4x and -4x), so they will be the easiest to eliminate when we add the equations together.

Solve the following using elimination. x-y=11 2x+y=19

• (10,-1)

• (-1,10)

• (-1,-10)

• (-10,-1)

Answer explanation

Solve using Elimination:

5x + y = 9

10x − 7y = −18

• (4, -11)

• (1, 4)

• (-1, 14)

• (-4, 29)

Answer explanation

7x - y = 10

-7x + y = -14

• No Solution

• (4, 1)

• Infinitely Many Solutions

• (2, -4)

Answer explanation

7x - y = 10

-7x + y = -14

All of the like terms have opposite coefficients, so both variables will be eliminated when we add the equations together. We cannot eliminate one without the other.

We are left with:

0=-4

This is a contradiction (false), so there is NO SOLUTION.

What is the best first step to solve this system by elimination?

• Add the equations to eliminate y

• Multiply the first equation by 2

• Multiply the second equation by 3

• Add the equations to eliminate x

What is the best first step to solve this system by elimination?

• Add the equations to eliminate y

• Multiply the first equation by 2

• Add the equations to eliminate x

What is the best first step to solve this system by elimination?

• Add the equations to eliminate y

• Multiply the first equation by 2

• Multiply the second equation by 2

• Add the equations to eliminate x

Solve the system by the elimination method.