Systems of Equations

Meaning

100

The form that is written in this format

y = mx + b

What is slope intercept form?

200

2 or more graphs on a coordinate plane

What is systems of equations?

300

The solution to the system of equations:

y = -3
x = 5

Write the answer as a coordinate pair

What is (5, -3)

400

The solution to a systems of equations is (3,-2).  What does that mean in terms of this problem?

What is where 2 or more linear equations cross or intersect on the coordinate plane?

500

When a graph has two lines that do not intersect, is called?

What is no solution?

Solving when variable is isolated

100

x = -2

y = x

(-2,-2)

y = x

y = -2

200

2x + 3y = 4

x = 3y + 2

What is (2, 0)?

300

y = -4x +6

2x + 3y= 18

(0, 6)

400

y = 2x + 4

x - y = -6

What is (2, 8)?

500

x = -6x -28

y = 3x + 4

(-4,-8)

Solving when both Equations are in slope intercept form

100

y=3x +2

y =2x - 2

(-4, - 10)

2x - 2 = 3x + 2

2x-2x - 2 = 3x - 2x + 2

-2 = x + 2

-2 -2 = x + 2 - 2

-4 = x

y = 3(-4) + 2

y = -12 + 2

y = -10

200

y = 5x + 10

y = 3x - 2

(-6,-20)

3x -2 = 5x + 10

3x -3x -2 -10 = 5x -3x + 10 - 10

-12 = 2x

-12/2 = 2x/2

-6=x

y =5(-6) + 10

y = -20

300

y = -6x

y = 3x

(0, 0)

3x = -6x

3x + 6x = -6x + 6x

9x = 0

x = 0

y = 3(0)

y = 0

400

y = -2x+6

y = 4x+12

(-1,8)

4x + 12 = -2x + 6

4x + 2x + 12 -12 = -2x + 2x + 6 - 12

6x/6 = -6/6

x = -1

y = -2(-1) + 6

y = 8

500

y = -3x - 15

y =-12x - 6

(1, - 18)

Can you do the Substitution Step

100

Substitute the following equations to solve for a variable

y = 3x + 2

2x + 3y = 12

What is 2x + 3(3x + 2) = 12

200

4x + 2y = 56

13x -2 = y

4x + 2(13x - 2) = 56

300

x = 13y + 2

2x -5y = 4

2(13y + 2) -5y = 4

400

2y - 4x +12 = 14

x = 6y - 10

2y - 4(6y - 10) + 12 = 14

500

- 5y = -12 - 2x

x = -2 +3y

-5y = -12 - 2(-2 + 3y)

Substitution

100

The solution to the system

y = 3x - 1
7x + 2y = 37

What is (3, 8)

7x + 2(3x - 1) = 37

7x + 6x - 2 = 37

13x -2+2 = 37 + 2

13x/13 = 39/13

x = 3

y = 3(3) -1

y = 8

200

The solution to the system

3x - 2y = 4
y = 2x - 1

What is (-2, -5)

3x -2(2x-1) = 4

3x -4x +2 = 4

-x +2-2 = 4-2

-x = 2

x = -2

y = 2(-2) -1

y = -5

300

The solution to the system

y +x = 12
y = (1/3)x

What is (9, 3)? 

(1/3)x + x = 12

4/3x = 12

x = 9

y =(1/3)9

y = 3

400

2x + 4y = 12

-3x +y = 24

(-6,6)

y = 3x + 24

2x + 4(3x + 24) = 12

2x + 12x + 96 = 12

14x = 12-96

14x = -84

x = -6

-3(-6)+y = 24

18+y =24

18-18+y =24-18

y = 6

500

5x + 2y = 16

4x + 2y = 10

(6, -7)     

 2y = 10 - 4x

2y/2 = 10/2 - 4x/2

y = 5 - 2x

5x + 2(5 - 2x) = 16

5x + 10 - 4x = 16

x + 10 -10 = 16 -10

x = 6

5(6) + 2y = 16

30 - 30 + 2y = 16 - 30

2y = -14

2y/2 = -14/2

y = -7