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

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(52790)   (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(20850)   (Show Source): You can put this solution on YOUR website!

----------------

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 are parallel and will never intersect. So there are no solutions and the system is inconsistent.

Answer by MathTherapy(10552)   (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_____ ------- eq (i)
2x + 4y = 32____2(x + 2y) = 2(16)_____x + 2y = 16____2y = - x + 16_____ ------- 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: , and will therefore be parallel, which means that there are no solutions to this system.
RELATED QUESTIONS
Solve the following system of equations by graphing x+2y=2... (answered by Fombitz)
solve the following system of equations by graphing 16x-4y=32... (answered by stanbon)
Solve the following system of equations by graphing x-2y=-4... (answered by fractalier)
3x-2y=8 2x-3y=7 solve each of the following system of equations by... (answered by checkley75,Edwin McCravy)
Solve the system of equations by graphing. 1=2x+y... (answered by jim_thompson5910)
Solve the following system of equations by graphing. x + 2y = 8 x + 2y = -4... (answered by richard1234)
Given the system of equations {{{system(x-4y=-12,y=-4+2x)}}} Solve the... (answered by jim_thompson5910)
Solve the following system of equations by graphing y=-1/2x-3... (answered by rothauserc)
Solve the system of equations by graphing x-2y=-4,... (answered by Fombitz)