SOLUTION: solve the following systems of equations graphically. x+y=3 5x-y=-3

Question 243567: solve the following systems of equations graphically.
x+y=3
5x-y=-3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.

Subtract from both sides.

Rearrange the terms.

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 -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1

So starting at

, go down 1 unit

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

---------------------------------------------------------------

Move onto the next equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

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 5 and the run is 1. This means that to go from point to point, we can go up 5 and over 1

So starting at

, go up 5 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

------------------------------------------------------------------

If we plot the two equations on the same coordinate axis, we get:

Graph of (red) and (green)

From the graph, we see that the two lines intersect at the point (0,3).

So the solution to the system

is (0,3). In other words, and are solutions.
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