Systems of Linear Equations

Substitution Method

100

Solve using the substitution method:

x = y

y = 0 - 9

x = -9

y = -9

(-9, -9)

200

Solve using the substitution method:

x = 3y - 1

2x + y = 12

x = 5

y = 2 

(5, 2)

300

Solve using the substitution method: 

7x + 2y = 3

x - 3y = 30

x = 3

y = -9

(3, -9)

400

Solve using the substitution method:

x + y + z = 30

2x + 3y + 4z = 90

x = y + 5

x = 35/3

y = 20/3

z = 35/3

(35/3, 20/3, 35/3)

Substitution Method

100

Solve using the substitution method:

x = 6y

y = 7

x = 42

y = 7

(42, 7)

200

Solve using the substitution method:

y = -2x + 5

3x - 2y = 4

x = 2

y = 1

(2, 1)

300

Solve using the substitution method:

x + 3y = 6

2x + 8y = -12

x = 42

y = -12

(42, -12)

400

Solve using the substitution method:

x - 2y + z = 0

2x + y - 3z = 5

x + 3y + 2z = 15

x = 11/3

y = 8/3

z = 5/3

(11/3, 8/3, 5/3)

Elimination Method

100

Solve using the elimination method:

x + y = 10

x - y = 2

x = 6

y = 4

(6, 4) 

200

Solve using the elimination method:

4x + 8y = 20

-4x + 2y = -30

x = 7

y = -1

(7, -1)

300

Solve using the elimination method:

2x + y = 7

3x + 2y = 12

x = 2

y = 3

(2, 3)

400

Solve using the elimination method:

x + y + z = 3

2x - y - z = 0

x + 2y - z = -1

x = 1

y = 0

z = 2

(1, 0, 2)

Elimination Method

100

Solve using the elimination method:

3x + 2y = 13

3x - 2y = 1

x = 7/3

y = 3

(7/3, 3)

200

Solve using the elimination method:

2x + 3y = 8

5x - 3y = 6 

x = 2

y = 4/3

(2, 4/3) 

300

Solve using the elimination method:

7x + 2y = 24

8x + 3y = 30

x = 12/5

y = 18/5

(12/5, 18/5)

400

Solve using the elimination method:

3x + 2y - 4z = 4

-2x + 3y + z = 12

x - 2y + 2z = -10

x = -2

y = 3

z = -1

(-2, 3, -1)

EXTRA QUESTIONS!

100

What are systems of linear equations?

Systems of linear equations are groups of two or more linear equations.

200

What are the two well-known methods of solving systems of linear equations?

The substitution method and the elimination method.

300

The _____ involves solving for a variable in one of the equations, then substituting the value for that variable into the 2nd equation in order to solve it.

substitution method

400

When we solve systems of linear equations, the solution is the _____ of the linear equations, which is the point where the lines cross.

intersection

500

*BONUS QUESTION*

The following system of linear equations is given:

x - 2y + z = 10

2x + 2y + 3z = 13

-2x + 5y + z = -7

What is the value of x + y + z?

4