# Thread: Solve for x

1. ## Solve for x

Its actually a trig question, but I'm having trouble with the algebra.

Solve for x
1st equation: x + y = 5 and 2nd equation: x^2/16 + y^2/9 = 1

My work so far...

sub y = x - 5 in to 2nd equation

x^2/16 + (x-5)^2/9 = 1

What do we do from here? Find the common denominator (144) and...

2. ## Re: Solve for x

Actually y = 5-x but it doesn't really matter.

Multiply both sides by 144, expand stuff, solve for x. Then plug your solution into x+y = 5 to find y.

4. ## Re: Solve for x

"Multiply both sides by 144, expand stuff, solve for x" is the part I'm struggling with...

5. ## Re: Solve for x

Originally Posted by durrrr
"Multiply both sides by 144, expand stuff, solve for x" is the part I'm struggling with...
Show us what you've done then...

6. ## Re: Solve for x

1st equation: x + y = 5 and 2nd equation: x^2/16 + y^2/9 = 1

y = x - 5

Sub into 2nd equation...

x^2/16 + (x-5)^2/9 = 1

9x^2/144 + ???/144 = 1

Sorry, I'm obviously not very good at math. I don't know what to do to the (x - 5). I'd really appreciate if somebody could finish the equation in baby steps. I understand the concept behind tangents and the actual question, there are obviously just gaping holes in my basic math knowledge when it comes to completing the solution.

7. ## Re: Solve for x

Originally Posted by durrrr
1st equation: x + y = 5 and 2nd equation: x^2/16 + y^2/9 = 1

y = x - 5

Sub into 2nd equation...

x^2/16 + (x-5)^2/9 = 1

9x^2/144 + ???/144 = 1

Sorry, I'm obviously not very good at math. I don't know what to do to the (x - 5). I'd really appreciate if somebody could finish the equation in baby steps. I understand the concept behind tangents and the actual question, there are obviously just gaping holes in my basic math knowledge when it comes to completing the solution.
Well if you've started by getting a common denominator of 144, then the numerator of the second equation needs to be multiplied by \displaystyle \begin{align*} 16 \end{align*}, giving \displaystyle \begin{align*} 16(x - 5)^2 \end{align*}. Now to expand the \displaystyle \begin{align*} (x - 5)^2 \end{align*}, use \displaystyle \begin{align*} (a - b)^2 = a^2 - 2ab + b^2 \end{align*}.