Solving Systems of Equations by Graphing Substitution and Elimination

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

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

• Parallel lines

• the same line 

• Intersecting lines

Solve the following system by graphing.  What is the solution?

• (3, -1)

• (-1, -3)

• (-1, -1)

• (-1, 3)

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

Solve by elimination

4x-6y= -6

-2x-12y= -12

• (0,1)

• (1,0)

• (1,1)

• (0, 2)

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.

Now determine what the solution to this system is!

• c = 12 s = 8

• c = 14 s = 8

• c = 8 s = 14

• c = 8 s = 12

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other.

Let x and y represent the number of yards each individual player rushed.

Now determine what the solution to the system is!

• x = 310 y = 1240

• x = 1240 y = 310

• x = 1545 y = 5

• x = 5 y = 1545

What is the first step in solving by elimination?

• To get variables that have the exact same coefficient.

• To get a variable alone.

• To get variables that have the same coefficient but opposite signs.