SOLUTION: Solve by graphing. x-y=5 x+y=3 Am I the only person that does not get graphing?

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Question 103016: Solve by graphing.
x-y=5
x+y=3
Am I the only person that does not get graphing?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Study this information hard and you will become expert.
Ed
Solved by pluggable solver: Graphing Linear Equations


1%2Ax-1%2Ay=5Start with the given equation



-1%2Ay=5-1%2Ax Subtract 1%2Ax from both sides

y=%28-1%29%285-1%2Ax%29 Multiply both sides by -1

y=%28-1%29%285%29%2B%281%29%281%29x%29 Distribute -1

y=-5%2B%281%29x Multiply

y=1%2Ax-5 Rearrange the terms

y=1%2Ax-5 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1 (the slope) and b=-5 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=1%2A%28-4%29-5

y=-4-5 Multiply

y=-9 Add

So here's one point (-4,-9)





Now lets find another point

Plug in x=-3

y=1%2A%28-3%29-5

y=-3-5 Multiply

y=-8 Add

So here's another point (-3,-8). Add this to our graph





Now draw a line through these points

So this is the graph of y=1%2Ax-5 through the points (-4,-9) and (-3,-8)


So from the graph we can see that the slope is 1%2F1 (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 1 units to get to the next point) the y-intercept is (0,-5)and the x-intercept is (5,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-5 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-5).


So we have one point (0,-5)






Now since the slope is 1%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-5), we can go up 1 units


and to the right 1 units to get to our next point



Now draw a line through those points to graph y=1%2Ax-5


So this is the graph of y=1%2Ax-5 through the points (0,-5) and (1,-4)

Solved by pluggable solver: Graphing Linear Equations


1%2Ax%2B1%2Ay=3Start with the given equation



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

y=%281%29%283-1%2Ax%29 Multiply both sides by 1

y=%281%29%283%29-%281%29%281%29x%29 Distribute 1

y=3-%281%29x Multiply

y=-1%2Ax%2B3 Rearrange the terms

y=-1%2Ax%2B3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1 (the slope) and b=3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-6

y=-1%2A%28-6%29%2B3

y=6%2B3 Multiply

y=9 Add

So here's one point (-6,9)





Now lets find another point

Plug in x=-5

y=-1%2A%28-5%29%2B3

y=5%2B3 Multiply

y=8 Add

So here's another point (-5,8). Add this to our graph





Now draw a line through these points

So this is the graph of y=-1%2Ax%2B3 through the points (-6,9) and (-5,8)


So from the graph we can see that the slope is -1%2F1 (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 1 units to get to the next point), the y-intercept is (0,3)and the x-intercept is (3,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,3).


So we have one point (0,3)






Now since the slope is -1%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,3), we can go down 1 units


and to the right 1 units to get to our next point



Now draw a line through those points to graph y=-1%2Ax%2B3


So this is the graph of y=-1%2Ax%2B3 through the points (0,3) and (1,2)

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



Start with the given system of equations:


1x-y=5

1x%2By=3





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-y=5 Start with the given equation



-y=5-x Subtract +x from both sides



-y=-x%2B5 Rearrange the equation



y=%28-x%2B5%29%2F%28-1%29 Divide both sides by -1



y=%28-1%2F-1%29x%2B%285%29%2F%28-1%29 Break up the fraction



y=x-5 Reduce



Now lets graph y=x-5 (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+x-5%29+ Graph of y=x-5




So let's solve for y on the second equation


1x%2By=3 Start with the given equation



1y=3-x Subtract +x from both sides



1y=-x%2B3 Rearrange the equation



y=%28-x%2B3%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%283%29%2F%281%29 Break up the fraction



y=-x%2B3 Reduce





Now lets add the graph of y=-x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-5%2C-x%2B3%29+ Graph of y=x-5(red) and y=-x%2B3(green)


From the graph, we can see that the two lines intersect at the point (4,-1) (note: you might have to adjust the window to see the intersection)