SOLUTION: 2x-4y=7 4x+2y=-1

Question 122678: 2x-4y=7
4x+2y=-1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Do you want to solve this using substitution?

Start with the given system of equations:

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

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Since , we can now replace each in the second equation with to solve for

For the second equation, replace with . Since this eliminates , we can now solve for .

Distribute to

Multiply

Multiply both sides by the LCM of 4. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)

Distribute and multiply the LCM to each side

Combine like terms on the left side

Add 14 to both sides

Combine like terms on the right side

Divide both sides by 20 to isolate x

Reduce

-----------------First Answer------------------------------

So the first part of our answer is:

-----------------------------------------------------------

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms and reduce. (note: if you need help with fractions, check out this solver)

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------------------------------------------------

-----------------Summary------------------------------

So our answers are:

and

which form the point

which as an ordered pair, look like:

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

we get

graph of (red) and (green) and the intersection of the lines (blue circle).

and we can see that the two equations intersect at

. This verifies our answer.

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