Algebra Club - CHART G - System of Equations

System of Equations

100

2x + y =7 

2x - 2y = -8

( 1, 5)

200

2x + 2y=4 

5y - 3x=6

( 1/2, 3/2)

300

164c + 24d = 4240 

d = 2c

(20, 40)

400

6x + 3y = 9 

-2x + y = -3

Infinite Solutions

500

u + 2v = 3 

4u + 8v = 12

Infinite Solutions

System of Equations

100

6x + 4y = 0 

6x + y = 9

(2, -3)

200

10x + 7y = 49 

10y - x = 70

(0, 7)

300

3w + 3f = 17.70 

2w + 3f = 15.55

(3.75, 2.15)

400

5u +7v = -25 

11u + 6v = -8

(2, -5)

500

x + y = 1 

x + 3y = 9

(-3, 4)

Vocabulary

100

Use when one equation is already

solved for a variable or can be easily

rearranged.

Substitution Method

200

Use when the equations are lined up in

standard form (Ax + By = C) and adding

or subtracting eliminates a variable.

Elimination Method

300

Systems of equations have how many solutions?

One

None

Infinity

400

A rectangular array of numbers.

Matrix

500

A matrix that includes the coefficients and constants from a system of equations.

Augmented Matrix

System of Equations

200

2x + y = 8 

y - x = 2

(4,2)

300

2x + y = 3 

x + 3y =12

( 3, -3)

400

12w + 10n = -14 

4w + 3n = -11

(1, -2)

500

5a -2b = 3 

2a - b = 0

(3, 6)

System of Equations

100

4y + 2x = 5 

x = 8 - 2y

No solutions. The system is inconsistent.

200

x + y = 20 

3x + 11y = 100

(15,5)

300

x + 3y = 3 

-x + y = -3

(3, 0)

400

2x + y = 1 

5x + 10y = -10

(0, 1)

500

x + 2y = 8 

x - 2y = 4

(6, 1)