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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (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,
-4%28Z%29=-8
Z=2
So multiplying the second equation by 2 will yield a parallel line.
a=2

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

2x-4y=6+
ax-8y=2
---------------------in slope-intercept form will be
+%282%2F4%29x-6%2F4=y+
%28a%2F8%29-2%2F8=y
------------------
%281%2F2%29x-3%2F2=y+ -> slope is %281%2F2%29
%28a%2F8%29-1%2F4=y -> slope is %28a%2F8%29
if lines are parallel there is no solution; so, for lines to be parallel, slopes must be equal
+%28a%2F8%29=%281%2F2%29 ...solve for+a
a=%281%2F2%298
a=4
then we have
2x-4y=6+
4x-8y=2
this system have no solution
check:
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-4y=6

4x-8y=2





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


2x-4y=6 Start with the given equation



-4y=6-2x Subtract 2+x from both sides



-4y=-2x%2B6 Rearrange the equation



y=%28-2x%2B6%29%2F%28-4%29 Divide both sides by -4



y=%28-2%2F-4%29x%2B%286%29%2F%28-4%29 Break up the fraction



y=%281%2F2%29x-3%2F2 Reduce



Now lets graph y=%281%2F2%29x-3%2F2 (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+%281%2F2%29x-3%2F2%29+ Graph of y=%281%2F2%29x-3%2F2




So let's solve for y on the second equation


4x-8y=2 Start with the given equation



-8y=2-4x Subtract 4+x from both sides



-8y=-4x%2B2 Rearrange the equation



y=%28-4x%2B2%29%2F%28-8%29 Divide both sides by -8



y=%28-4%2F-8%29x%2B%282%29%2F%28-8%29 Break up the fraction



y=%281%2F2%29x-1%2F4 Reduce





Now lets add the graph of y=%281%2F2%29x-1%2F4 to our first plot to get:


Graph of y=%281%2F2%29x-3%2F2(red) and y=%281%2F2%29x-1%2F4(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.