Systems by Substitution, Elimination, and Combining

Solve the system:
x + 6y = 17
x - 3y = 8

• (5, 2)

• (11, 1)

• (1, 11)

• no solution

Solve the system:
2x + 3y = -2
3x - 2y = 23

• (5, -4)

• (-4, 5)

• (-5, 4)

• infinite solutions

What is the Solution to this system?

• (2,-2)

• (-2,2)

• All Real Numbers

• No Solution

True or False:

To solve a system of equations using the elimination method, we need to get one of the variables to cancel (for example 2x and -2x).

• True

• False

Which method would probably be best to solve this system of equations? y = 4x + 1 3x + 2y = 13

• Graphing

• Substitution

• Elimination

If you use the substitution method, which of the following would be the correct substitution?

y = 4x + 1

3x + 2y = 13

• 3(4x + 1) +2y = 13

• 3x + 2(4x + 1) = 13

If I am solving by elimination, is this system "ready to go" where I can eliminate one of the variables immediately? If so, which variable can I eliminate?

4x + 9y = 28

-4x - y = -28

• Yes, "x" can be eliminated immediately.

• Yes, "y" can be eliminated immediately.

• No, neither variable is "ready to go."

Is this system of equations "ready to go" where you can eliminate one variable right now? If so, which variable can I eliminate immediately?

• Yes, I can eliminate the "x" immediately.

• Yes, I can eliminate the "y" immediately.

• No, I can't eliminate either variable immediately.

Which of the following would be a good first step to solve this problem by elimination?

• Multiply the top equation by -13

• Multiply the top equation by -1

• Multiply the top equation by 4

• Multiply the top equation by 12

What would my system of equations look like after multiplying the top equation by 4?

• -4x + 4y = -4

  -8x - 4y = -8

• -4x + 4y = -52

  -8x - 4y = -8

• -8x + 8y = -17

  -8x - 4y = -8

• -5x + 5y = -60

  -8x - 4y = -8