Solving System with Two Variables

x − y = 11
2x + y = 19

• (-1, 10)

• (30, 19)

• (19, 30)

• (10, -1)

-x - 7y = 14
-4x - 14y = 28

• (-2, 0)

• (0, -2)

• (-2, -2)

• (0, 2)

If two lines are parallel how many solutions do they have?

• 1

• 2

• infinite

• none

Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4

• YES

• NO

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Answer explanation

The lines intersect at (1,3) so that is the solution.

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.

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