SOLUTION: Given the two systems, 2x-4y=6 and ax-8y=2. What should be the value of a be in order for the equations to have no solution

Question 1012421: Given the two systems, 2x-4y=6 and ax-8y=2. What should be the value of a be in order for the equations to have no solution
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
No solution means the lines are parallel.
So the left hand side of the second equation would be a multiple of the left hand side of the first.
Comparing the y coefficients,

So multiplying the second equation by 2 will yield a parallel line.

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

---------------------in slope-intercept form will be

------------------
-> slope is
-> slope is
if lines are parallel there is no solution; so, for lines to be parallel, slopes be
...solve for

then we have

this system have solution
check:

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.

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