# If 2x+3y=1, what is x/2+y/3 in terms of y?

Oct 24, 2016

$\frac{3 - 5 y}{12}$

Note that as a fraction question is asked, a fraction answer should be given.

#### Explanation:

The phrase " in terms of " means "using".

A fraction is given, but it contains both $x \mathmr{and} y$ variables, we only want $y$.

From the equation which is given, $2 x + 3 y = 1$, we can find an expression for x "in terms of " y.

$2 x = 1 - 3 y \text{ } \rightarrow x = \frac{1 - 3 y}{2}$

Replace $x$ with this fraction in $\frac{x}{2} + \frac{y}{3}$

$\left(\frac{1 - 3 y}{2}\right) \div 2 + \frac{y}{3}$

=$\frac{1 - 3 y}{4} + \frac{y}{3} \text{ } \leftarrow$ find the LCD

=$\frac{3 \left(1 - 3 y\right) + 4 y}{12}$

=$\frac{3 - 9 y + 4 y}{12}$

=$\frac{3 - 5 y}{12}$