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?

Algebra ->  Linear-equations -> 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?      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

if you have x%2B3y=4
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


1%2Ax%2B3%2Ay=4Start with the given equation



3%2Ay=4-1%2Ax Subtract 1%2Ax from both sides

y=%281%2F3%29%284-1%2Ax%29 Multiply both sides by 1%2F3

y=%281%2F3%29%284%29-%281%2F3%29%281%29x%29 Distribute 1%2F3

y=4%2F3-%281%2F3%29x Multiply

y=%28-1%2F3%29%2Ax%2B4%2F3 Rearrange the terms

y=%28-1%2F3%29%2Ax%2B4%2F3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1%2F3 (the slope) and b=4%2F3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%28-1%2F3%29%2A%28-8%29%2B4%2F3

y=8%2F3%2B4%2F3 Multiply

y=12%2F3 Add

y=4 Reduce

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





Now lets find another point

Plug in x=-5

y=%28-1%2F3%29%2A%28-5%29%2B4%2F3

y=5%2F3%2B4%2F3 Multiply

y=9%2F3 Add

y=3 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 y=%28-1%2F3%29%2Ax%2B4%2F3 through the points (-8,4) and (-5,3)


So from the graph we can see that the slope is -1%2F3 (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 (0,1.33333333333333) ,or (0,4%2F3), and the x-intercept is (4,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=4%2F3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,4%2F3).


So we have one point (0,4%2F3)






Now since the slope is -1%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,4%2F3), 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 y=%28-1%2F3%29%2Ax%2B4%2F3


So this is the graph of y=%28-1%2F3%29%2Ax%2B4%2F3 through the points (0,1.33333333333333) and (3,0.333333333333333)





steps to solve a system by graphing:
your system is
2x-y=1....eq.1
x%2B3y=4....eq.2

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



Start with the given system of equations:


1x%2B3y=4

2x-y=1





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


1x%2B3y=4 Start with the given equation



3y=4-x Subtract +x from both sides



3y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%284%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B4%2F3 Reduce



Now lets graph y=%28-1%2F3%29x%2B4%2F3 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B4%2F3%29+ Graph of y=%28-1%2F3%29x%2B4%2F3




So let's solve for y on the second equation


2x-y=1 Start with the given equation



-y=1-2x Subtract 2+x from both sides



-y=-2x%2B1 Rearrange the equation



y=%28-2x%2B1%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%281%29%2F%28-1%29 Break up the fraction



y=2x-1 Reduce





Now lets add the graph of y=2x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B4%2F3%2C2x-1%29+ Graph of y=%28-1%2F3%29x%2B4%2F3(red) and y=2x-1(green)


From the graph, we can see that the two lines intersect at the point (1,1) (note: you might have to adjust the window to see the intersection)