91Ó°ÊÓ

We have an equation$y^2-5y-11=13$and a set$y:\left\{2,4,6,8,10\right\}$

To find the solution of the given equation.

We substitute the values of y in the given equation one by one and check which value of y makes both the sides of the equation equal.

Which value of y makes both the sides of the equation that is called the solution of the given equation.

Substitute $y=2$in the given equation.

$2^2-5×2-11=13$

$⇒4-10-11=13$

$⇒-17≠13$

Therefore, $y=2$is not the solution of the given equation.

Substitute $y=4$in the given equation.

$4^2-5×4-11=13$

$⇒16-20-11=13$

$⇒-15≠13$

Therefore, $y=4$is not the solution of the given equation.

Substitute $y=6$in the given equation.

$6^2-5×6-11=13$

$⇒36-30-11=13$

$⇒-5≠13$

Therefore, $y=6$is not the solution of the given equation.

Substitute $y=8$in the given equation.

$8^2-5×8-11=13$

$⇒64-40-11=13$

$⇒13=13$

Therefore, $y=8$is a solution of the given equation.

Substitute $y=10$in the given equation.

${10}^2-5×10-11=13$

$⇒100-50-11=13$

$⇒39≠13$

Therefore, $y=10$is not the solution of the given equation.