SOLUTION: 2x+3y=24 y+7x=46 Im stuck from the very begining...

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Question 141086: 2x+3y=24
y+7x=46
Im stuck from the very begining...
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Do you want to use substitution to solve this?

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.

Start with the second equation (Either equation will work, but y is easier to isolate in this equation)

Subtract from both sides

Rearrange the equation

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

Since , we can now replace each in the first 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

Combine like terms on the left side

Subtract 138 from both sides

Combine like terms on the right side

Divide both sides by -19 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

-----------------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).