Systems of Linear Equations Workshop

Definitions

100

An ordered pair that satisfies both equations in the system.

A solution

200

A linear system that has at least one solution is called...

A consistant system

300

A linear system with no solution is called...

An inconsistant sytem

400

How can the solution of the system be found by graphing?

Where the lines touch or cross.

Solution or not?

100

Is the solution (4,-1)?

x+2y=2

x-2y=6

Yes

200

Is the soluton (7,6)?

2x-3y=-4

2x+y=4

No, not a solution.

300

Is the solution (-3,5)?

9x+7y=8

8x-9y=-69

Yes!

400

Is the solution (2,5)?

2x+3y=17

x+4y=16

No!  Not a solution.

Solve by Substitution

100

5x-4y=9

x-2y=-3

(5,4)

200

2x-3y=-13

y=2x+7

(-2,3)

300

x=3y+7

x-2y-1

(-17,-8)

400

2x+5y=-4

3x-y=11

(3,-2)

Solve by Elimination

100

x+y=7

x-y=-1

(3,4)

200

3x-4y=11

-3x+2y=-7

(1,-2)

300

3x+2y=48

9x-8y=-24

(8,12)

400

2x+3y=-16

5x-10y=30

(-2,-4)

Consistant and Inconsitant

100

4x+6y=12

6x+9y=12

Inconsistant!  No solution!

200

x=9-2y

x+2y=13

Inconsistant.  (No solutution)

300

y=3x-2

15x-5y=10

Consistant.  Infinite solutions.

400

y=3x-5

21x-35=7y

Consistant.  Infinite solutions.