Solving Systems of Equations by Addition or Subtraction

A solution of the system 2x+y=7 and 5x-y=14 is (3, 1). How are the graphs of the two equations related?

• The graphs are parallel.

• The graphs coincide.

Put a check on the box that denotes the method of solving systems of linear equations in two variables.

Note: You can choose one or more answers.

• Graphing Method

• Addition Method

• Subtraction Method

• Elimination Method

• Substitution Method

The method of solving systems of linear equations where inverses/opposites are used to eliminate one of the variables.

• Elimination Method

• Substitution Method

• Graphing Method

• Addition Method

• Subtraction Method

Complete the statement below: An independent linear system is _______________________

• a system with equations that are identical

• a system with exactly one solution

• a system of lines

• a system with equations that are satisfied by every real number

What equation will you get when adding both equations?

• 10x = -3

• 10x -8y = -3

• 0 = -3

Find the solution to this system.

4x + 8y = 20

−4x + 2y = −30

• (-1, 7)

• (-7, 1)

• (7, -1)

• (1, -7)

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.

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