SOLUTION: Does this system of equations have one solution, no solutions, or an infinite number of solutions?2y + 8x - 12 = 0 ----------- ----------- -4x + y = -6

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Does this system of equations have one solution, no solutions, or an infinite number of solutions?2y + 8x - 12 = 0 ----------- ----------- -4x + y = -6       Log On


   

Question 1049542: Does this system of equations have one solution, no solutions, or an infinite number of solutions?2y + 8x - 12 = 0
-------------------------4x + y = -6 [an infinite number of solutions],[no solution],[one solution]
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
It has one and only one solution.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y+%2B+8x+-+12+=+0
4x+%2B+y+=+-6+
--------------------------------
y+%2B+8x+=+12
4x+%2B+y+=+-6+
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2B8y=12

4x%2By=-6





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%2B8y=12 Start with the given equation



8y=12-x Subtract +x from both sides



8y=-x%2B12 Rearrange the equation



y=%28-x%2B12%29%2F%288%29 Divide both sides by 8



y=%28-1%2F8%29x%2B%2812%29%2F%288%29 Break up the fraction



y=%28-1%2F8%29x%2B3%2F2 Reduce



Now lets graph y=%28-1%2F8%29x%2B3%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+%28-1%2F8%29x%2B3%2F2%29+ Graph of y=%28-1%2F8%29x%2B3%2F2




So let's solve for y on the second equation


4x%2By=-6 Start with the given equation



1y=-6-4x Subtract 4+x from both sides



1y=-4x-6 Rearrange the equation



y=%28-4x-6%29%2F%281%29 Divide both sides by 1



y=%28-4%2F1%29x%2B%28-6%29%2F%281%29 Break up the fraction



y=-4x-6 Reduce





Now lets add the graph of y=-4x-6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F8%29x%2B3%2F2%2C-4x-6%29+ Graph of y=%28-1%2F8%29x%2B3%2F2(red) and y=-4x-6(green)


From the graph, we can see that the two lines intersect at the point (-60%2F31,54%2F31) (note: you might have to adjust the window to see the intersection)


so, [one solution]