SOLUTION: Solve the system of equations by the substitution method. 5x+15y=10 2x+8y=6 The solution is: (Type an ordered pair. Type integers or simplified fractions. Type

Question 131038: Solve the system of equations by the substitution method.
5x+15y=10

2x+8y=6
The solution is:
(Type an ordered pair. Type integers or simplified fractions. Type N if there is no solution. Type I if there are infinitely many solutions.)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Multiply both sides by the LCM of 3. 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

Subtract 16 from both sides

Combine like terms on the right side

Divide both sides by -2 to isolate x

Divide

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

Now let's graph the two equations (if you need help with graphing, check out this solver)

From the graph, we can see that the two equations intersect at

. This visually verifies our answer.

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

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