Harwood Integrated Math 2 (Linear Systems)

Graphing

100

y = 2x + 2

y = x - 1

(-3, -4)

200

y = 2x + 4

y = 3x + 2

(2, 8)

300

x = 3

y = 2x + 1

(3, 7)

400

y = 1/2x + 2

y - 5 = 1/4(x - 4)

(8,6)

500

4x + 2y = 8

2x + y = 4

Infinitely many solutions

Substitution

100

y = 2

3x + 2y = 10

(2, 2)

200

x =-3y +2

x - 2y = -3

(-1, 1)

300

x - 2y = -10

y = 3x

(2, 6)

400

-2x + 3y = 2

 y = -4x + 24

(5, 4)

500

3y = 15x + 39

-5x +y = 24

no solution

Elimination

100

x + 3y = 5

2x -3y = -8

(-1, 2)

200

5x + 8y = 82

5x + 2y = 58

(10, 4)

300

-3x + 5y = 14

4x + 10y = 48

(2, 4)

400

3x−4y=8

18x−5y=10

(0, -2)

500

4x−9y−2=0

12x−5y+38=0

(-4, -2)

Miscellaneous

100

What point are we sure the line y-7=3(x-5) goes through?

(5,7)

200

What is the x-intercept of -3x+5y=12

-4

300

Solve for x:

4(2x+1)+7=35

x=3

400

Which method is most efficient to solve the following system of equations?

2x+3y=24

y=4x+10

Substitution

500

Solve for y:

3x-4y=24

y=3/4x-6

Vocab

100

Two or more equations to be solved simultaneously. 

System of equations 

200

The method of solving equations where you add or subtract equations to end up with one variable.

Elimination

300

When solving a system of equations using a graph, the solution can be found at the point of ____________. 

intersection

400

If a system of equations has no solution they have the same ______ and different _________. 

slope; y-intercepts

500

If a system of linear equations has infinitely many solutions, they are _____________. 

the same line (equivalent equations)