SOLUTION: Solve the following system of equations by graphing and find the intersection point. X+3y=4 and 2x-y=1 How do I get X's and Y's to plot on the graph?

Question 957265: Solve the following system of equations by graphing and find the intersection point.
X+3y=4 and 2x-y=1
How do I get X's and Y's to plot on the graph?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

if you have
to get X's and Y's to plot on the graph, you choose values for X's and calculate Y's
here are the steps to graph a linear function:

Solved by pluggable solver: Graphing Linear Equations

Start with the given equation

Subtract from both sides

Multiply both sides by

Distribute

Multiply

Rearrange the terms

Reduce any fractions

So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

Multiply

Add

Reduce

So here's one point (-8,4)

Now lets find another point

Plug in x=-5

Multiply

Add

Reduce

So here's another point (-5,3). Add this to our graph

Now draw a line through these points

So this is the graph of through the points (-8,4) and (-5,3)

So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 3 units to get to the next point), the y-intercept is (0,) ,or (0,), and the x-intercept is (,0) . So all of this information verifies our graph.

We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,).

So we have one point (0,)

Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go down 1 units

and to the right 3 units to get to our next point

Now draw a line through those points to graph

So this is the graph of through the points (0,1.33333333333333) and (3,0.333333333333333)

steps to solve a system by graphing:
your system is
....eq.1
....eq.2

Solved by pluggable solver: Solve the System of Equations by Graphing

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

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

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 add the graph of to our first plot to get:

Graph of (red) and (green)

From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

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