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

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) (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) (Show Source): You can put this solution on YOUR website!

1.
,
......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:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

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

2.

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

Start with the given system of equations:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

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

3.

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

Start with the given system of equations:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

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

4.
(5,0)...here you have a point (x,y)= (5,0)

.......(5,0) is not solution, point doesn't lie on given line

5.
(-4,1)

.......point doesn't lie on given line

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