SOLUTION: Solve each of the following by graphing 2x+y=8 2x-y=0

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Question 107769: Solve each of the following by graphing
2x+y=8
2x-y=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solve each of the following by graphing
2x+%2B+y+=+8
here is the graph:

Solved by pluggable solver: Graphing Linear Equations


2%2Ax%2B1%2Ay=8Start with the given equation



1%2Ay=8-2%2Ax Subtract 2%2Ax from both sides

y=%281%29%288-2%2Ax%29 Multiply both sides by 1

y=%281%29%288%29-%281%29%282%29x%29 Distribute 1

y=8-%282%29x Multiply

y=-2%2Ax%2B8 Rearrange the terms

y=-2%2Ax%2B8 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-2 (the slope) and b=8 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=0

y=-2%2A%280%29%2B8

y=0%2B8 Multiply

y=8 Add

So here's one point (0,8)





Now lets find another point

Plug in x=1

y=-2%2A%281%29%2B8

y=-2%2B8 Multiply

y=6 Add

So here's another point (1,6). Add this to our graph





Now draw a line through these points

So this is the graph of y=-2%2Ax%2B8 through the points (0,8) and (1,6)


So from the graph we can see that the slope is -2%2F1 (which tells us that in order to go from point to point we have to start at one point and go down -2 units and to the right 1 units to get to the next point), the y-intercept is (0,8)and the x-intercept is (4,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=8 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,8).


So we have one point (0,8)






Now since the slope is -2%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,8), we can go down 2 units


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



Now draw a line through those points to graph y=-2%2Ax%2B8


So this is the graph of y=-2%2Ax%2B8 through the points (0,8) and (1,6)





2x+-+y+=+0
here is the graph:
Solved by pluggable solver: Graphing Linear Equations


2%2Ax-1%2Ay=0Start with the given equation



-1%2Ay=0-2%2Ax Subtract 2%2Ax from both sides

y=%28-1%29%280-2%2Ax%29 Multiply both sides by -1

y=%28-1%29%280%29%2B%281%29%282%29x%29 Distribute -1

y=0%2B%282%29x Multiply

y=2%2Ax%2B0 Rearrange the terms

y=2%2Ax%2B0 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=2 (the slope) and b=0 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=2%2A%28-4%29%2B0

y=-8%2B0 Multiply

y=-8 Add

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





Now lets find another point

Plug in x=-3

y=2%2A%28-3%29%2B0

y=-6%2B0 Multiply

y=-6 Add

So here's another point (-3,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=2%2Ax%2B0 through the points (-4,-8) and (-3,-6)


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


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


So we have one point (0,0)






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


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



Now draw a line through those points to graph y=2%2Ax%2B0


So this is the graph of y=2%2Ax%2B0 through the points (0,0) and (1,2)