Question

Find x
4 (x - 2y) - (5x + 3y) = 30
3 (3x + 7y) - 2 ( x + 9y ) = 12

Answer 1

`x = 3`

Explanation:

Expand and rewrite both equations to make y the subject:

`\begin{aligned}4(x-2y)-(5x+3y) & =30\\\implies 4x-8y-5x-3y & =30\\4x-5x-8y-3y & =30\\-x-11y & =30\\x+11y & = -30\\ 11y & = -x-30\\ y & = (-x-30)/(11)\end{aligned}`

`\begin{aligned}3(3x+7y)-2(x+9y) & = 12\\\implies 9x+21y-2x-18y & = 12 \\9x-2x+21y-18y & = 12\\7x+3y & = 12 \\3y & = -7x+12\\ y & = -(7)/(3)x+4\end{aligned}`

Now solve for
`x` by substitution:

`\begin{aligned}y & = y\\\\\implies (-x-30)/(11) & = -(7)/(3)x+4\\\\-x-30 & = 11\left(-(7)/(3)x+4\right)\\\\-x-30 & = -(77)/(3)x+44\\\\-x+(77)/(3)x & =44+30\\\\(74)/(3)x & = 74\\\\74x & = 222\\\\x & = (222)/(74)\\\\x & =3 \end{aligned}`