SOLUTION: Another graphing question. I tried to do this and got (4,4) Obviously it was wrong. The problem is 2x+y=5 3x-y=10 Please and Thank You=)

Algebra ->  Graphs -> SOLUTION: Another graphing question. I tried to do this and got (4,4) Obviously it was wrong. The problem is 2x+y=5 3x-y=10 Please and Thank You=)      Log On


   

Question 130092This question is from textbook algebra
: Another graphing question. I tried to do this and got (4,4) Obviously it was wrong.


The problem is
2x+y=5 3x-y=10
Please and Thank You=) This question is from textbook algebra

Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
2X+Y=5 OR Y=-2X+5 (RED LINE)
3X-Y=10 OR -Y=-3X+10 OR Y=3X-10 (GREEN LINE)
ANSWER (3,-1)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-2x+%2B5%2C+3x+-10%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -2x +5 and 3x -10).

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

2x%2By=5
3x-y=10




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

2x%2By=5 Start with the given equation


y=5-2x Subtract 2+x from both sides


y=-2x%2B5 Rearrange the equation



Now lets graph y=-2x%2B5




Looking at y=-2x%2B5 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-2 and the y-intercept is b=5


Since b=5 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -2, this means:

rise%2Frun=-2%2F1


which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1



So starting at , go down 2 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=-2x%2B5

So this is the graph of y=-2x%2B5 through the points and





So let's solve for y on the second equation

3x-y=10 Start with the given equation


-y=10-3x Subtract 3+x from both sides


-y=-3x%2B10 Rearrange the equation


y=%28-3x%2B10%29%2F%28-1%29 Divide both sides by -1


y=%28-3%2F-1%29x%2B%2810%29%2F%28-1%29 Break up the fraction


y=3x-10 Reduce



Now lets graph y=3x-10





Looking at y=3x-10 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=3 and the y-intercept is b=-10


Since b=-10 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is 3, this means:

rise%2Frun=3%2F1


which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1



So starting at , go up 3 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=3x-10

So this is the graph of y=3x-10 through the points and




Now let's graph the two equations together on the same coordinate system



Graph of y=-2x%2B5(red) and y=3x-10(green)


From the graph, we can see that the two lines intersect at the point (3,-1)