SOLUTION: Identify the solution(s) of the system of equations, if any -3x-4y=2 8y =-6x-4

Algebra ->  Linear-equations -> SOLUTION: Identify the solution(s) of the system of equations, if any -3x-4y=2 8y =-6x-4       Log On


   

Question 841698: Identify the solution(s) of the system of equations, if any
-3x-4y=2
8y =-6x-4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
-3x-4y=2+
8y+=-6x-4
___________________
-3x-4y=2+
6x%2B8y+=-4
_____________________

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-3x-4y=2

6x%2B8y=-4





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


-3x-4y=2 Start with the given equation



-4y=2%2B3x Add 3+x to both sides



-4y=%2B3x%2B2 Rearrange the equation



y=%28%2B3x%2B2%29%2F%28-4%29 Divide both sides by -4



y=%28%2B3%2F-4%29x%2B%282%29%2F%28-4%29 Break up the fraction



y=%28-3%2F4%29x-1%2F2 Reduce



Now lets graph y=%28-3%2F4%29x-1%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+%28-3%2F4%29x-1%2F2%29+ Graph of y=%28-3%2F4%29x-1%2F2




So let's solve for y on the second equation


6x%2B8y=-4 Start with the given equation



8y=-4-6x Subtract 6+x from both sides



8y=-6x-4 Rearrange the equation



y=%28-6x-4%29%2F%288%29 Divide both sides by 8



y=%28-6%2F8%29x%2B%28-4%29%2F%288%29 Break up the fraction



y=%28-3%2F4%29x-1%2F2 Reduce





Now lets add the graph of y=%28-3%2F4%29x-1%2F2 to our first plot to get:


Graph of y=%28-3%2F4%29x-1%2F2(red) and y=%28-3%2F4%29x-1%2F2(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.