Question

Solve the equation. Check your solution.

$\mathbf{13}\mathbf{y}\mathbf{+}\mathbf{19}\mathbf{=}\mathbf{54}\mathbf{+}\mathbf{6}\mathbf{y}\mathbf{+}\mathbf{14}$

Short answer

The solution for the equation $13y+19=54+6y+14$ is $y=7$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}13y+19=54+6y+14\\ 13y+19-19=+6y+68-19\left(\text{Subtract19frombothsides}\right)\\ 13y+0=6y+49\left(\text{Simplify}\right)\\ 13y-6y=6y-6y+49\left(\text{Subtract6yfrombothsides}\right)\\ 7y=49\left(\text{Simplify}\right)\end{array}$

– Solve for y

Now, divide both sides of the equation by 7.

$\begin{array}{c}\frac{7y}{7}=\frac{49}{7}\\ y=7\end{array}$

Therefore, the solution of the equation is $y=7$.

– Check the solution 

To check the solution, write the original equation and substitute the value of y.

$13y+19=54+6y+14$

Now, substitute $y=7$and check the result.

$\begin{array}{c}13\times 7+19=54+6\times 7+14\\ 91+19=54+42+14\\ 110=110\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.