SOLUTION: what is the graphical solution of the equation x-y=-2,x=3y=14

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Question 104487: what is the graphical solution of the equation x-y=-2,x=3y=14
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the graphical solution of the equation
1.
x+-+y+=+-2
Solved by pluggable solver: Graphing Linear Equations


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



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

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

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

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

y=1%2Ax%2B2 Rearrange the terms

y=1%2Ax%2B2 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-9

y=1%2A%28-9%29%2B2

y=-9%2B2 Multiply

y=-7 Add

So here's one point (-9,-7)





Now lets find another point

Plug in x=-8

y=1%2A%28-8%29%2B2

y=-8%2B2 Multiply

y=-6 Add

So here's another point (-8,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=1%2Ax%2B2 through the points (-9,-7) and (-8,-6)


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 (0,2)and the x-intercept is (-2,0) . So all of this information verifies our graph.


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


So we have one point (0,2)






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 (0,2), 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%2B2


So this is the graph of y=1%2Ax%2B2 through the points (0,2) and (1,3)



2.
x+-+3y+=+14 I guess, here is -3y
Solved by pluggable solver: Graphing Linear Equations


1%2Ax-3%2Ay=14Start with the given equation



-3%2Ay=14-1%2Ax Subtract 1%2Ax from both sides

y=%28-1%2F3%29%2814-1%2Ax%29 Multiply both sides by -1%2F3

y=%28-1%2F3%29%2814%29%2B%281%2F3%29%281%29x%29 Distribute -1%2F3

y=-14%2F3%2B%281%2F3%29x Multiply

y=%281%2F3%29%2Ax-14%2F3 Rearrange the terms

y=%281%2F3%29%2Ax-14%2F3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F3 (the slope) and b=-14%2F3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-7

y=%281%2F3%29%2A%28-7%29-14%2F3

y=-7%2F3-14%2F3 Multiply

y=-21%2F3 Add

y=-7 Reduce

So here's one point (-7,-7)





Now lets find another point

Plug in x=-4

y=%281%2F3%29%2A%28-4%29-14%2F3

y=-4%2F3-14%2F3 Multiply

y=-18%2F3 Add

y=-6 Reduce

So here's another point (-4,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=%281%2F3%29%2Ax-14%2F3 through the points (-7,-7) and (-4,-6)


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 up 1 units and to the right 3 units to get to the next point) the y-intercept is (0,-4.66666666666667) ,or (0,-14%2F3), and the x-intercept is (14,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-14%2F3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-14%2F3).


So we have one point (0,-14%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,-14%2F3), we can go up 1 units


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



Now draw a line through those points to graph y=%281%2F3%29%2Ax-14%2F3


So this is the graph of y=%281%2F3%29%2Ax-14%2F3 through the points (0,-4.66666666666667) and (3,-3.66666666666667)