Question

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

$\mathbf{5}\mathbf{x}-\mathbf{2}\mathbf{y}-\mathbf{1}=\mathbf{0}$

Short answer

The required solution is $y=\frac{5x-1}{2}$.

Step-by-step solution

– State the concept

An equation solved for y gives an equation wherey 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 $5x-2y-1=0$.

– Solve for y 

$5x-2y-1=0$(Given equation)

$5x-2y-1+2y=0+2y$(Add $2y$ to both sides)

$5x-1=2y$ (Simplify)

$2y=5x-1$ (Rearrange)

$\frac{2y}{2}=\frac{5x-1}{2}$(Divide both sides by 2)

$y=\frac{5x-1}{2}$(Simplify)

So, the required solution is $y=\frac{5x-1}{2}$.