Question

Fact checking

3/5x + 1/4y= -1/2

Would equal y=x+-1

Right?

Answer 1

just an addition to the great posting above

`\cfrac{3}{5}x+\cfrac{1}{4}y~~ = ~~-\cfrac{1}{2}\implies \cfrac{3x}{5}+\cfrac{1y}{4}~~ = ~~-\cfrac{1}{2}\implies \cfrac{3x}{5}+\cfrac{y}{4}~~ = ~~-\cfrac{1}{2}`

now, hmmm let's look at the denominators, hmmm 5, 4 and 2, so hmm we can get an LCD of 20 from that, now, let's multiply both sides by that LCD to do away with the denominators.

`\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{3x}{5}+\cfrac{y}{4} \right)~~ = ~~20\left( -\cfrac{1}{2} \right)}\implies 12x+5y~~ = ~~-10 \implies 5y=-12x-10 \\\\\\ y=\cfrac{-12x-10}{5}\implies y=\cfrac{-12x}{5}-\cfrac{10}{5}\implies y=-\cfrac{12}{5}x-2`

Answer 2

y =
`(-12)/(5)` - 2

Explanation:

`(3x)/(5)` +
`(1)/(4)`y =
`(-1)/(2)` Subtract
`(3x)/(5)` from both sides of the equation

`(1y)/(4)` =
`(-3x)/(5)` -
`(1)/(2)` Multiple all the way through by 4

y =
`(-12x)/(5)` - 2