SOLUTION: the problem that I am solving through substitution is 9x + 2y = -51(equation 1) and -9x + y =69(equation 2), I substituted with a fraction in place of x and also got a fraction for

Question 376347: the problem that I am solving through substitution is 9x + 2y = -51(equation 1) and -9x + y =69(equation 2), I substituted with a fraction in place of x and also got a fraction for y and it was wrong, how do I properly calculate fraction answers at this point?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

Which form the ordered pair

.

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of (red) and (green)

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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