Systems of Equations

Vocabulary

100

More than one equation to be solved at the same time is know as this.

System of Equations

200

The ratio of rise to run is called the..

Slope

300

What is the name of "b" in y = mx + b?

Y-intercept

400

y = mx + b is more formally known as this.

Slope-intercept form

500

What is the answer to an equation or system of equations?

Solution

Solving by Graphing or Substitution

100

Solve the systems of equations below. 

y = x + 4
y = 2x + 5

(-1, 3)

200

The solution to the system of equations:

y = 3x - 2
y = -x - 2

(0, -2)

300

The solution to the system of equations:

y - 3x = 3
y = 3x - 2

No solution

400

Find the solution to the system of equations. 

y = (1/3)x - 3
2x - y = 8

(3, -2)

500

The solution to the system of equations:

y = -3
x = 5

(5, -3)

Solving by Elimination

100

The solution to the system of equations:

x + y = -6
x - y = -10

(-8, 2)

200

The solution to the system:

8x + 5y = 9
2x - 5y = -4

(1/2, 1)

or 

(0.5, 1)

300

The solution to the system:

2x + y = 7 

x + 5y = 17

(2, 3)

400

The solution to the system:

2x + 3y = 6
3x + 5y = 15

(-15, 12)

500

The solution to the system:

2x - 4y = 12
-8x + 16y = -48

Infinitely many solutions

Solving by Substitution

100

The solution to the system:

x = 4y
2x + 3y = 22

(8, 2)

200

The solution to the system

y = x - 2
3x - y = 16

(7, 5)

300

The solution to the system

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

(3, 8)

400

The solution to the system

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

(-2, -5)

500

The solution to the system

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

(3, 9)