SOLUTION: Could you please help me with the steps,in this kind of problem? I know that I have to solve each system graphically,but I have been sick and don't remember how to work them.Thank

Algebra ->  Rational-functions -> SOLUTION: Could you please help me with the steps,in this kind of problem? I know that I have to solve each system graphically,but I have been sick and don't remember how to work them.Thank       Log On


   

Question 124889: Could you please help me with the steps,in this kind of problem? I know that I have to solve each system graphically,but I have been sick and don't remember how to work them.Thank you in advance.LH
1) x-y=3
x+y=5
2)3x+y=5
x-2y=4
3)4y=x+8
3x-2y=6
4)x=y-1
2x=3y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started

# 1

Start with the given system of equations:

1x-y=3
1x%2By=5




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=3 Start with the given equation


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


-y=-x%2B3 Rearrange the equation


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


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


y=x-3 Reduce


Now lets graph y=x-3 (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-3%29+ Graph of y=x-3



So let's solve for y on the second equation

1x%2By=5 Start with the given equation


1y=5-x Subtract +x from both sides


1y=-x%2B5 Rearrange the equation


y=%28-x%2B5%29%2F%281%29 Divide both sides by 1


y=%28-1%2F1%29x%2B%285%29%2F%281%29 Break up the fraction


y=-x%2B5 Reduce



Now lets add the graph of y=-x%2B5 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-3%2C-x%2B5%29+ Graph of y=x-3(red) and y=-x%2B5(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)







# 2





Start with the given system of equations:

3x%2By=5
1x-2y=4




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

3x%2By=5 Start with the given equation


1y=5-3x Subtract 3+x from both sides


1y=-3x%2B5 Rearrange the equation


y=%28-3x%2B5%29%2F%281%29 Divide both sides by 1


y=%28-3%2F1%29x%2B%285%29%2F%281%29 Break up the fraction


y=-3x%2B5 Reduce


Now lets graph y=-3x%2B5 (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+-3x%2B5%29+ Graph of y=-3x%2B5



So let's solve for y on the second equation

1x-2y=4 Start with the given equation


-2y=4-x Subtract +x from both sides


-2y=-x%2B4 Rearrange the equation


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


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


y=%281%2F2%29x-2 Reduce



Now lets add the graph of y=%281%2F2%29x-2 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B5%2C%281%2F2%29x-2%29+ Graph of y=-3x%2B5(red) and y=%281%2F2%29x-2(green)

From the graph, we can see that the two lines intersect at the point (2,-1) (note: you might have to adjust the window to see the intersection)