SOLUTION: Solve the system using any algebraic method. x-y=17 1/2x-3y=1

Question 215116: Solve the system using any algebraic method.
x-y=17
1/2x-3y=1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Multiply EVERY term by the LCD 2 to clear out the fraction.

So we have the system of equations:

Start with the first equation.

Subtract from both sides.

Divide both sides by to isolate .

Rearrange the terms and simplify.

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

Move onto the second equation.

Now plug in .

Distribute.

Combine like terms on the left side.

Subtract from 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 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 .

This means that the system is consistent and independent.

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