y
3
=5x
+7
y = -x – 9
y
3
=5x
+7
This system
can be solved
quickly by
graphing.
y = -x – 9
y
3
=5x
+7
Plot the
y-intercept of
the first
equation.
y = -x – 9
•
y
3
=5x
+7
y = -x – 9
5 right
Use the slope
to plot a second
point from the
first equation.
•
3 up
•
y
3
=5x
+7
Connect the
two points to
graph the line
for the first
equation.
y = -x – 9
•
•
y
3
=5x
+7
Plot the
y-intercept of
the second
equation.
y = -x – 9
•
•
•
y
3
=5x
+7
Use the slope
to plot a second
point from the
second
equation.
y = -1x – 9
•
••
1 left
1 up
•
y
3
=5x
+7
Connect the
two points to
graph the line
for the second
equation.
y = -x – 9
•
••
•
y
3
=5x
+7
Look at the
point of
intersection and
write the
coordinates of
that point.
(-10, 1)
y = -x – 9
•
•
••
•
2x – 3y = -12
y = -3x – 7
2x – 3y = -12
y = -3x – 7
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
x = -3
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
x = -3
y = -3x – 7
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
x = -3
y = -3x – 7
y = -3•-3 – 7
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
x = -3
y = -3x – 7
y = -3•-3 – 7
y=9–7
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
x = -3
y = -3x – 7
y = -3•-3 – 7
y=9–7
y=2
2x – 3y = -12
y = -3x – 7
2x – 3(-3x – 7) = -12
2x – 3(-3x – 7) = -12
2x + 9x + 21 = -12
11x = -33
x = -3
y = -3x – 7
y = -3•-3 – 7
y=9–7
(-3, 2)
y=2
5x – 3y = 20
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
8x = 48
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
3x + 3y = 28
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
3x + 3y = 28
3•6 + 3y = 28
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
3x + 3y = 28
3•6 + 3y = 28
18 + 3y = 28
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
3x + 3y = 28
3•6 + 3y = 28
18 + 3y = 28
3y = 10
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
3x + 3y = 28
3•6 + 3y = 28
18 + 3y = 28
3y = 10
y = 3.3
5x – 3y = 20
3x + 3y = 28
8x = 48
x=6
(6, 3.3)
3x + 3y = 28
3•6 + 3y = 28
18 + 3y = 28
3y = 10
y = 3.3
6x + 8y = 4
9x + 10y = 7
6x + 8y = 4
3(6x + 8y) = 3(4)
9x + 10y = 7
6x + 8y = 4
3(6x + 8y) = 3(4)
9x + 10y = 7
-2(9x + 10y) = -2(7)
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
9x + 10y = 7
-2(9x + 10y) = -2(7)
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8•-0.5 = 4
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8•-0.5 = 4
6x + -4 = 4
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8•-0.5 = 4
6x + -4 = 4
6x = 8
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8•-0.5 = 4
6x + -4 = 4
6x = 8
x = 1.3
6x + 8y = 4
3(6x + 8y) = 3(4)
18x + 24y = 12
-18x + -20y = -14
4y = -2
y = -0.5
(-0.5, 1.3)
9x + 10y = 7
-2(9x + 10y) = -2(7)
-18x + -20y = -14
6x + 8y = 4
6x + 8•-0.5 = 4
6x + -4 = 4
6x = 8
x = 1.3
Three ways to solve a system of
linear equations are:
graphing
substitution
linear combination.
Each method can be useful depending
on the system being solved.