y
2
=3x
+4
Two equations
are written
above.
We can graph
both equations.
y = -3x – 7
y
2
=3x
+4
Two equations
are written
above.
We can graph
both equations.
y = -3x – 7
•
y
2
=3x
+4
Two equations
are written
above.
We can graph
both equations.
y = -3x – 7
3 right
•
2 up
•
y
2
=3x
+4
Two equations
are written
above.
We can graph
both equations.
y = -3x – 7
•
•
y
2
=3x
+4
Two equations
are written
above.
We can graph
both equations.
y = -3x – 7
•
•
y
2
=3x
+4
Two equations
are written
above.
y = -3x – 7
•
We can graph
both equations.
•
•
y
2
=3x
+4
Two equations
are written
above.
y = -3x – 7
•
We can graph
both equations.
•
•
1 left
3 up
•
y
2
=3x
+4
Two equations
are written
above.
y = -3x – 7
•
We can graph
both equations.
•
•
•
y
2
=3x
+4
The point
where the two
lines intersect
is a solution
common to
both equations.
y = -3x – 7
•
•
•
•
y
2
=3x
+4
The point
where the two
lines intersect
is a solution
common to
both equations.
The point is the
solution to the
system of
equations.
y = -3x – 7
•
•
•
•
y
2
=3x
+4
The point
where the two
lines intersect
is a solution
common to
both equations.
The point is the
solution to the
system of
equations.
y = -3x – 7
•
•
•
•
y
2
=3x
+4
The point is the
solution to the
system of
equations.
In this case:
(-3, 2)
y = -3x – 7
•
•
•
•
•
3x + 4y = 12
3x – 8y = 48
3x + 4y = 12
We can use the
intercepts to
graph the first
equation.
3x – 8y = 48
3x + 4y = 12
We can use the
intercepts to
graph the first
equation.
If x = 0, then
y = 3.
3x – 8y = 48
•
3x + 4y = 12
We can use the
intercepts to
graph the first
equation.
If y = 0, then
x = 4.
3x – 8y = 48
•
•
3x + 4y = 12
3x – 8y = 48
•
•
3x + 4y = 12
For the second
equation,
if x = 0, then
y = -6.
3x – 8y = 48
•
•
•
3x + 4y = 12
For the second
equation,
if y = 0, then
x = 16, but that
won't fit on our
grid.
3x – 8y = 48
•
•
•
3x + 4y = 12
Remember that
if an equation
is in standard
form the slope
is:
-A
B
3x – 8y = 48
•
•
•
3x + 4y = 12
Remember that
if an equation
is in standard
form the slope
is:
-A
B
-3 = 3
8
-8
3x – 8y = 48
•
•
•
3x + 4y = 12
We could also
rewrite the
equation in
slope-intercept
form:
y = 83 x – 6
3x – 8y = 48
•
•
•
3x + 4y = 12
We could also
rewrite the
equation in
slope-intercept
form:
y = 83 x – 6
3x – 8y = 48
•
•
8 right
3 up
•
•
3x + 4y = 12
3x – 8y = 48
•
•
•
•
3x + 4y = 12
The point is the
solution to the
system of
equations.
3x – 8y = 48
•
•
•
•
3x + 4y = 12
The point is the
solution to the
system of
equations.
3x – 8y = 48
•
In this case:
(8, -3)
•
•
•
3(2x + 4y) = 12
4x + 8y = 48
3(2x + 4y) = 12
4x + 8y = 48
3(2x + 4y) = 12
3
3
4x + 8y = 48
3(2x + 4y) = 12
3
3
4x + 8y = 48
3(2x + 4y) = 12
3
2x + 4y = 4
3
4x + 8y = 48
3(2x + 4y) = 12
3
3
2x + 4y = 4
x-intercept = 2
y-intercept = 1
4x + 8y = 48
3(2x + 4y) = 12
3
3
2x + 4y = 4
x-intercept = 2
y-intercept = 1
4x + 8y = 48
x-intercept = 12
y-intercept = 6
3(2x + 4y) = 12
First equation:
x-intercept = 2
y-intercept = 1
4x + 8y = 48
3(2x + 4y) = 12
4x + 8y = 48
First equation:
x-intercept = 2
y-intercept = 1
•
3(2x + 4y) = 12
4x + 8y = 48
First equation:
x-intercept = 2
y-intercept = 1
••
3(2x + 4y) = 12
4x + 8y = 48
First equation:
x-intercept = 2
y-intercept = 1
••
3(2x + 4y) = 12
4x + 8y = 48
Second equation:
x-intercept = 12
y-intercept = 6
••
3(2x + 4y) = 12
4x + 8y = 48
Second equation:
x-intercept = 12
y-intercept = 6
••
•
3(2x + 4y) = 12
4x + 8y = 48
Second equation:
x-intercept = 12
y-intercept = 6
•
••
•
3(2x + 4y) = 12
4x + 8y = 48
Second equation:
x-intercept = 12
y-intercept = 6
•
••
•
3(2x + 4y) = 12
The lines are
parallel.
There is no
solution.
ø
4x + 8y = 48
•
••
•
Graphing is a good visual way
to show common solutions of
equations that form lines.
It works well when the solutions
are integers close to zero.
It also is a good way to get
approximate solutions when
exact solutions are not required.