SOLUTION: Solve the equations for x and y or state that there is no solution. 3x + 7y = 5 2x

SOLUTION: Solve the equations for x and y or state that there is no solution. 3x + 7y = 5 2x - y = 1

Question 183044: Solve the equations for x and y or state that
there is no solution.
3x + 7y = 5
2x - y = 1

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 second equation

Start with the second 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 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

Add 7 to both sides

Combine like terms on the right side

Divide both sides by 17 to isolate x

-----------------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 (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 ordered pair

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