Question

Solve each equation for $\mathbf{y}$.

$\mathbf{3}\mathbf{x}-\mathbf{5}\mathbf{y}+\mathbf{4}=\mathbf{0}$

Short answer

The required solution is $y=\frac{3x+4}{5}$.

Step-by-step solution

– State the concept

An equation solved for $y$ gives an equation where $y$ is the only thing on the left-hand side and the other terms are on the right-hand side.

– List the given data

The given equation is $3x-5y+4=0$.

– Solve for y 

$3x-5y+4=0$(Given equation)

$3x-5y+4+5y=0+5y$(Add $5y$ to both sides)

$3x+4=5y$ (Simplify)

$5y=3x+4$ (Rearrange)

$\frac{5y}{5}=\frac{3x+4}{5}$(Divide both sides by 5)

$y=\frac{3x+4}{5}$ (Simplify)

So, the required solution is $y=\frac{3x+4}{5}$.