Systems Review Day 1

​Systems of Equations Review Day 1

​Solving with Substitution

1. ​Locate x = or y =.

2. Substitute that expression in to the 2nd equation and solve for the variable.

3. Substitute that answer in to one of the original equations and solve for the other variable.​

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Solve using substitution.

y = 5x + 22

y = -2x - 6

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Solve using substitution.

-4x - 4y = 8

y = 4x - 17

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Solve using substitution.

x - 3y = 19

5x + 8y = -20

​Solving with Elimination

1. ​Locate or create a common coefficient for a variable.

2. Add or Subtract to eliminate the variable with the common coefficient.

3. Solve for the remaining variable.

4. Substitute that answer in to one of the original equations and solve for the other variable.​

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Solve using elimination.

x + 6y = -5

-x + 9y = 5

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Solve using elimination.

-x - 2y = 10

-x - y = 10

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Solve using elimination.

-x + 2y = 3

2x - y = 3

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Solve using elimination.

-3x + 3y = 15

-5x + 8y = 22

​Solving with 3 Variables

1. Eliminate one of your 3 variables in all 3 equations.

2. Solve the new 2 variable system using either elimination or substitution.

3. Substitute your answers in to one of the original equations and solve for the third variable.​

​Or use your graphing calculator and your matrices.

Fill in the Blank

Solve the system.

-4x = 12

z = -3x - 10

x = -3y - 6z + 6

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Solve the system.

-2x - z = -8

6x + 2y - 2z = 24

y = -3x + z - 2

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Solve the system.

6x - 2y + 5z = 17

4y + 6z = 2

-5x + 2z = 11

Multiple Choice

John’s school is selling tickets to a musical.  The first day they sold 13 adult tickets and 14 student tickets for a total of $281.  The second day they sold 13 adult tickets and 9 student tickets for a total of $241. What is the price of each ticket?

• Adult tickets are $13 and student tickets are $8.

• Adult tickets are $8 and student tickets are $13.

• Adult tickets are $11 and student tickets are $10.

• Adult tickets are $10 and student tickets are $11.