Expert: Bobby Soltani - 9/7/2004

Question
Hello Bobby.
Here is the question that I need your help for...

If 9X - 3Y = 12 and 3X - 5Y = 7, then 6X - 2Y equals...?

I look forward to your answer. Thanks.

Naomi

Answer
Hi Naomi,

For this equation, we have two equations and two unknowns (X and Y).  Here's how we solve these.

Solve the first one in terms of Y.
9X-3Y=12
subtract 9x from both sides
-3y = 12-9x
divide both sides by -3
y = 3x-4
Now, plug this value for y into the second equation

3x-5(3x-4) = 7
solve for x
3x-15x+20 = 7
-12x = -13
x = 13/12
plug this value for x into either equation to get y
9*(13/12) - 3y =12
39/4 - 3y = 12
-3y = 9/4
y = -3/4

So, we have x = 13/12 and y = -3/4.  To find 6X-2Y, we have
6(13/12) - 2*(-3/4)
13/2 + 3/2 = 16/2 = 8

That's it.  Let me know if you have questions.

Bobby