Question

I need a bit of help on this sim question

Answer 1

Given:

`\begin{gathered} x^2+y^2=25\ldots\ldots(1) \\ x+y=7\ldots\ldots\text{.}(2) \end{gathered}`

To solve for x and y:

Using the formula,

`(x+y)^2=x^2+y^2+2xy`

Substitute the given values we get,

`\begin{gathered} 7^2=25+2xy \\ 2xy=49-25 \\ 2xy=24 \\ xy=12 \\ y=(12)/(x)\ldots\ldots\ldots(3) \end{gathered}`

Substitute equ (3) in (2), we get,

`\begin{gathered} x+(12)/(x)=7 \\ (x^2+12)/(x)=7 \\ x^2+12=7x \\ x^2-7x+12=0 \\ (x-4)(x-3)=0 \\ x=4(or)3 \end{gathered}`

Substitute x=4 and x=3 in equation (3) we get,

`\begin{gathered} y=(12)/(4) \\ y=3 \\ y=(12)/(3) \\ y=4 \end{gathered}`

Hence, the solutions are,

`(4,\text{ 3) and (3,4)}`