Graphing #1
Graphing #2
6 7
Substitution #1
Substitution #2
How Many Solutions
100
Solve by graphing.
y=3x-2
y=-3x+4
(1,1)
100
Solve by graphing.
y=7/2x-3
y=1/2x+3
(2,4)
100
Does the system of equations have a solution of (6,7)?
y=2x-5
x-y=-1
Yes!
100
Solve by substitution.
y=6x
y=x-5
(-1,-6)
100
Solve by substitution.
y=-2x
y=x-3
(1,-2)
100
y=2x+4
y=-2x-7
One Solution; different slope, different lines, so they must intersect!
200
Solve by graphing.
y=3x+4
y=-3x-2
(-1,1)
200
Solve by graphing.
y=1/3x+2
y=-1/3x+4
(3,3)
200
Solve by graphing:
y=6x-7
y=-7x+6
(1, -1)
200
Solve by substitution.
y=7x+17
y=-3x-3
(-2,3)
200
Solve by substitution.
y=-8
-2x+4y=-22
(-5,-8)
200
2x+y=4
y=-2x+6
No solution; when rearranged, we can see these lines have the same slope but different y-intercepts
300
Solve by graphing.
y=-x+4
-6x+y=-3
(1,3)
300
Solve by graphing.
y=-x+3
5x+y=-1
(-1,4)
300
Solve by graphing:
y=6x+7
y=6x-7
No Solution
300
Solve by substitution.
y=0
-x+2y=-7
(7,0)
300
Solve by substitution.
y=3x+22
-5x-7y=-24
(-5,7)
300
y=4x-5
y=4x+3
No Solution ; same slope but different y-intercepts means parallel lines!
400
Solve by graphing.
8x+3y=12
2x+3y=-6
(3,-4)
400
Solve by graphing.
5x-3y=12
2x+3y=9
(3,1)
400
Solve by substitution.
x=3
6x+7y=67
(3, 7)
400
Solve by substitution.
y=8x+4
3x-2y=5
(-1,-4)
400
Solve by substitution.
3x+y=6
-3x-8y=-6
(2,0)
400
y=3x-5
-2y-10=-6x
Infinite Solutions! When rewritten, these are the same equation.
500
Solve by graphing.
-2y=-7x+8
-4+2y=x
(2,3)
500
Solve by graphing.
-y+2=2x
-3y-x=9
(3,-4)
500
Solve by substitution:
2x+y=19
x-y=-1
(6,7)
500
Solve by substitution.
5x+y=1
6x-4y=22
(1,-4)
500
Solve by substitution.
4x-6y=20
-x-2y=2
(2,-2)
500
x=5y
y + 4 = 1/5x + 4
Infinite Solutions