SOLUTION: PLEASE HELP .. I'm trying to help my son w/his hw.. I need answers/solutions to refresh my memory !! 1. x+y=4, 2x+y=5 2. x-y=5, 2x+3y=0 3. x-y=-2, x+y=4 4. y=x+3 (5,0) 5. y

Algebra ->  Equations -> SOLUTION: PLEASE HELP .. I'm trying to help my son w/his hw.. I need answers/solutions to refresh my memory !! 1. x+y=4, 2x+y=5 2. x-y=5, 2x+3y=0 3. x-y=-2, x+y=4 4. y=x+3 (5,0) 5. y      Log On


   

Question 689019: PLEASE HELP .. I'm trying to help my son w/his hw..
I need answers/solutions to refresh my memory !!
1. x+y=4, 2x+y=5
2. x-y=5, 2x+3y=0
3. x-y=-2, x+y=4
4. y=x+3 (5,0)
5. y=2x+3 (-4,1)
Found 2 solutions by ankor@dixie-net.com, MathLover1:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1.
x + y = 4
2x + y = 5
------------subtraction eliminates y, find x
-x = -1
x = 1
find y
1 + y = 4
y = 4 - 1
y = 3
Check solution of x=1; y=3, in the 2nd equation
2(1) + 3 = 5
:
2.
x - y = 5
2x + 3y = 0
Use substitution with the first equation here
x - y = 5
x = y+5
replace x with y+5 in the 2nd equation
2(y+5) + 3y = 0
2y + 10 + 3y = 0
2y + 3y = -10
5y = -10
y = -10/5
y = -2
find x using x = y + 5
x = -2 + 5
x = 3
check solution of x=3; y=-2 in the 2nd equation
2(3) + 3(-2) = 0
6 - 6 = 0
:
3.
x - y = -2
x + y = 4
----------------addition eliminates y, find x
2x = 2
x = 1
I'll let you find y, check your solutions in both equations
:
I'm not sure what (5,0) or (-4,1) mean here, they can't be an x/y pair
4. y = x + 3 (5,0)
5. y = 2x + 3 (-4,1)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.
x%2By=4,
2x%2By=5......here you have system of two linear functions
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=4

2x%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%2By=4 Start with the given equation



1y=4-x Subtract +x from both sides



1y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%284%29%2F%281%29 Break up the fraction



y=-x%2B4 Reduce



Now lets graph y=-x%2B4 (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%2B4%29+ Graph of y=-x%2B4




So let's solve for y on the second equation


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



1y=5-2x Subtract 2+x from both sides



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



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



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



y=-2x%2B5 Reduce





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%2C-2x%2B5%29+ Graph of y=-x%2B4(red) and y=-2x%2B5(green)


From the graph, we can see that the two lines intersect at the point (1,3) (note: you might have to adjust the window to see the intersection)



2.
x-y=5
2x%2B3y=0

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



Start with the given system of equations:


1x-y=5

2x%2B3y=0





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


2x%2B3y=0 Start with the given equation



3y=0-2x Subtract 2+x from both sides



3y=-2x%2B0 Rearrange the equation



y=%28-2x%2B0%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%280%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x%2B0 Reduce





Now lets add the graph of y=%28-2%2F3%29x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-5%2C%28-2%2F3%29x%2B0%29+ Graph of y=x-5(red) and y=%28-2%2F3%29x%2B0(green)


From the graph, we can see that the two lines intersect at the point (3,-2) (note: you might have to adjust the window to see the intersection)



3.
x-y=-2
x%2By=4
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-y=-2

1x%2By=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


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



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



-y=-x-2 Rearrange the equation



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



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



y=x%2B2 Reduce



Now lets graph y=x%2B2 (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%2B2%29+ Graph of y=x%2B2




So let's solve for y on the second equation


1x%2By=4 Start with the given equation



1y=4-x Subtract +x from both sides



1y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%284%29%2F%281%29 Break up the fraction



y=-x%2B4 Reduce





Now lets add the graph of y=-x%2B4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2%2C-x%2B4%29+ Graph of y=x%2B2(red) and y=-x%2B4(green)


From the graph, we can see that the two lines intersect at the point (1,3) (note: you might have to adjust the window to see the intersection)



4.
y=x%2B3 (5,0)...here you have a point (x,y)= (5,0)
0=5%2B3
0=8.......(5,0) is not solution, point doesn't lie on given line


5.
y=2x%2B3 (-4,1)
1=2%28-4%29%2B3
1=-8%2B3
1=-5.......point doesn't lie on given line