SOLUTION: Solve {{{system(4x-5y=-28,-9x-2y=10)}}}

Question 191954: Solve

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:

Start with the first equation.

Subtract from both sides.

Divide both sides by to isolate .

Break up the fraction.

Reduce.

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

Now plug in into the second equation.

Distribute.

Multiply EVERY term by the LCD to clear any fractions.

Multiply.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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

Since we know that , we can use this to find .

Go back to the first isolated equation

Plug in .

Multiply.

Combine the fractions

Combine like terms.

Reduce.

So the solutions are and .

which form the ordered pair (-2,4)

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)

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