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Graphing

100

The point where two lines intersect on a graph

the solution

200

y=x+2 and y + -x+4

 (1, 3)

300

The y-intercept of the line y=1/2 x - 4

(0, -4)

400

y=2x - 1 and y = - x+5

(2, 3)

500

To solve 2x - y = 4  by graphing, you must first rewrite it in this form.

 slope-intercept form (y=mx+b)

Substitution

100

y=2x and 3x + y =10

substituting 2x for y in the second equation

200

y=3x and x + 2y=14

(2, 6)

300

x=y - 1 and 2x + y=10

(3, 4)

400

y=4x + 2 and y=2x+6

(2, 10)

500

solve 2x + 3y=12 and y = x - 4

(24/5,4/5)

Elimination

100

x + y=10 and x-y=2

(6, 4)

200

2x + y =7 and x + y=4

(3, 1)

300

3x + 2y =10  and 2x - 2y =10

(4, -1)

400

4x + 3y= 1 and 3x + 2y=1 

(1, -1)

500

To eliminate x in the system 3x + 4y=10 and 2x + 3y=7 you can multiply the equations by these numbers.

2 and -3

Special Cases (No/Infinite Solutions)

100

If two lines are parallel and have different y-intercepts, the system has this many solutions.

no solution

200

 If both equations represent the same line, the system has this many solutions.

 infinitely many solutions

300

Identify the number of solutions:y=2x + 1 and y= 2x + 5

no solution