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Start with the given system of equations:
In order to graph these equations, we need to solve for y for each equation.
So let's solve for y on the first equation
Start with the given equation
Subtract
from both sides
Rearrange the equation
Now lets graph
Looking at
we can see that the equation is in slope-intercept form
where the slope is
and the y-intercept is
Since
this tells us that the y-intercept is
)
.Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is
, this means:
which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1
So starting at
, go down 2 units
and to the right 1 unit to get to the next point
)
Now draw a line through these points to graph
So this is the graph of
through the points
and
So let's solve for y on the second equation
Start with the given equation
Subtract
from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
Now lets graph
Looking at
we can see that the equation is in slope-intercept form
where the slope is
and the y-intercept is
Since
this tells us that the y-intercept is
)
.Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is
, this means:
which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1
So starting at
, go up 3 units
and to the right 1 unit to get to the next point
)
Now draw a line through these points to graph
So this is the graph of
through the points
and
Now let's graph the two equations together on the same coordinate system
Graph of
(red) and
(green)
From the graph, we can see that the two lines intersect at the point (3,-1)
(