SOLUTION: how do i solve -4x-y=y and 3x-y=0 in subsitution form.

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Question 399717: how do i solve -4x-y=y and 3x-y=0 in subsitution form.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-4x-y=y ...add -y to the both sides

-4x-y+-y=y-y
-4x-2y+=+0
now solve in substitution form:
-4x-2y+=+0
3x-y=0+

Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

-4%2Ax-2%2Ay=0
3%2Ax-1%2Ay=0

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

-2%2Ay=0%2B4%2AxAdd 4%2Ax to both sides

y=%280%2B4%2Ax%29%2F-2 Divide both sides by -2.


Which breaks down and reduces to



y=0-2%2Ax Now we've fully isolated y

Since y equals 0-2%2Ax we can substitute the expression 0-2%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B-1%2Ahighlight%28%280-2%2Ax%29%29=0 Replace y with 0-2%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax-1%2A%280%29-1%28-2%29x=0 Distribute -1 to 0-2%2Ax

3%2Ax%2B0%2B2%2Ax=0 Multiply



3%2Ax%2B0%2B2%2Ax=0 Reduce any fractions

3%2Ax%2B2%2Ax=0%2B0Add 0 to both sides


3%2Ax%2B2%2Ax=0 Combine the terms on the right side



5%2Ax=0 Now combine the terms on the left side.


cross%28%281%2F5%29%285%2F1%29%29x=%280%2F1%29%281%2F5%29 Multiply both sides by 1%2F5. This will cancel out 5%2F1 and isolate x

So when we multiply 0%2F1 and 1%2F5 (and simplify) we get



x=0 <---------------------------------One answer

Now that we know that x=0, lets substitute that in for x to solve for y

3%280%29-1%2Ay=0 Plug in x=0 into the 2nd equation

0-1%2Ay=0 Multiply

-1%2Ay=0%2B0Add 0 to both sides

-1%2Ay=0 Combine the terms on the right side

cross%28%281%2F-1%29%28-1%29%29%2Ay=%280%2F1%29%281%2F-1%29 Multiply both sides by 1%2F-1. This will cancel out -1 on the left side.

y=0%2F-1 Multiply the terms on the right side


y=0 Reduce


So this is the other answer


y=0<---------------------------------Other answer


So our solution is

x=0 and y=0

which can also look like

(0,0)

Notice if we graph the equations (if you need help with graphing, check out this solver)

-4%2Ax-2%2Ay=0
3%2Ax-1%2Ay=0

we get


graph of -4%2Ax-2%2Ay=0 (red) and 3%2Ax-1%2Ay=0 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (0,0). This verifies our answer.


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Check:

Plug in (0,0) into the system of equations


Let x=0 and y=0. Now plug those values into the equation -4%2Ax-2%2Ay=0

-4%2A%280%29-2%2A%280%29=0 Plug in x=0 and y=0


0%2B0=0 Multiply


0=0 Add


0=0 Reduce. Since this equation is true the solution works.


So the solution (0,0) satisfies -4%2Ax-2%2Ay=0



Let x=0 and y=0. Now plug those values into the equation 3%2Ax-1%2Ay=0

3%2A%280%29-1%2A%280%29=0 Plug in x=0 and y=0


0%2B0=0 Multiply


0=0 Add


0=0 Reduce. Since this equation is true the solution works.


So the solution (0,0) satisfies 3%2Ax-1%2Ay=0


Since the solution (0,0) satisfies the system of equations


-4%2Ax-2%2Ay=0
3%2Ax-1%2Ay=0


this verifies our answer.