SOLUTION: can someone please help me? solve each system by the substitution method. 10. 4x+2y=-8 2x+y=-4

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Question 487417: can someone please help me?

solve each system by the substitution method.
10. 4x+2y=-8
2x+y=-4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
4x%2B2y=-8.......1


2x%2By=-4..........2

----------------------
2x%2By=-4..........2...solve for y
y=-2x-4...substitute in 1
4x%2B2%28-2x-4%29=-8.......1..solve for x
4x-4x-8=-8
4x-4x=-8%2B8
0=0.......there are an infinite number of solutions and the system is dependent
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


4x%2B2y=-8

2x%2By=-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


4x%2B2y=-8 Start with the given equation



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



2y=-4x-8 Rearrange the equation



y=%28-4x-8%29%2F%282%29 Divide both sides by 2



y=%28-4%2F2%29x%2B%28-8%29%2F%282%29 Break up the fraction



y=-2x-4 Reduce



Now lets graph y=-2x-4 (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+-2x-4%29+ Graph of y=-2x-4




So let's solve for y on the second equation


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



1y=-4-2x Subtract 2+x from both sides



1y=-2x-4 Rearrange the equation



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



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



y=-2x-4 Reduce





Now lets add the graph of y=-2x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x-4%2C-2x-4%29+ Graph of y=-2x-4(red) and y=-2x-4(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.