Q35 - Geometry

Question

Find the value of the variable.

$5y=3y+26$

Step-by-Step Solution

Answer

The value of the variable is $\mathit{y}\mathbf{=}\mathbf{13}$.

Step 1. Subtract 3y.

First subtract 3y from both sides of the equation $5y=3y+26$. 

$5y-\left(3y\right)=3y+26-\left(3y\right)$

Step 2. Combine the like terms.

To further simplify open the brackets and combine the like terms.

$\begin{array}{l}5y-3y=3y-3y+26\\ 2y=26\end{array}$

Step 3. Divide by 2.

Divide both sides of the equation $2y=26$ by 2 and cancel the common factors of 2 on both sides.

$\begin{array}{l}\frac{2y}{2}=\frac{26}{2}\\ y=\frac{13\times 2}{2}\\ y=13\end{array}$

Step 4. Verify the value.

In order to verify the value of y, substitute 13 for y into the equation $5y=3y+26$.

$\begin{array}{l}5\times 13=3\times 13+26\\ 65=39+26\\ 65=65\text{ True}\end{array}$

Hence, the value of the variable is $y=13$.