SOLUTION: Solve the following system of equations by graphing. x+2y=8 2x+4y=32

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Question 1089057: Solve the following system of equations by graphing.
x+2y=8
2x+4y=32
Found 3 solutions by ikleyn, MathLover1, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The system is inconsistent.

There are no solutions.


Look: the coefficients of the second equation are doubled of that of the first equation.

But the right hand side constant term is nod doubled.

Therefore, the solutions do not exist.


See the lesson
    - Geometric interpretation of a linear system of two equations in two unknowns
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".



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

x%2B2y=8
2x%2B4y=32
----------------
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2B2y=8

2x%2B4y=32





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%2B2y=8 Start with the given equation



2y=8-x Subtract +x from both sides



2y=-x%2B8 Rearrange the equation



y=%28-x%2B8%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%288%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B4 Reduce



Now lets graph y=%28-1%2F2%29x%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+%28-1%2F2%29x%2B4%29+ Graph of y=%28-1%2F2%29x%2B4




So let's solve for y on the second equation


2x%2B4y=32 Start with the given equation



4y=32-2x Subtract 2+x from both sides



4y=-2x%2B32 Rearrange the equation



y=%28-2x%2B32%29%2F%284%29 Divide both sides by 4



y=%28-2%2F4%29x%2B%2832%29%2F%284%29 Break up the fraction



y=%28-1%2F2%29x%2B8 Reduce





Now lets add the graph of y=%28-1%2F2%29x%2B8 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B4%2C%28-1%2F2%29x%2B8%29+ Graph of y=%28-1%2F2%29x%2B4(red) and y=%28-1%2F2%29x%2B8(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the following system of equations by graphing.
x+2y=8
2x+4y=32
x + 2y = 8____2y = - x + 8_____matrix%281%2C3%2C+y%2C+%22=%22%2C+%28-+1%2F2%29x+%2B+4%29 ------- eq (i)

2x + 4y = 32____2(x + 2y) = 2(16)_____x + 2y = 16____2y = - x + 16_____matrix%281%2C3%2C+y%2C+%22=%22%2C+%28-+1%2F2%29x+%2B+8%29 ------- eq (ii)

Substitute 0 for x in eq (i) to get the y-intercept. Then substitute 0 for y to get the x-intercept.

Plot the points

Join the points

Repeat the process for eq (ii)

You'll see that the linear graphs have the same slope: -+1%2F2, and will therefore be parallel, which means that there are no solutions to this system.