Question

Find the solution of each equation if the replacement sets are $x:\left\{1,3,5,7,9\right\}$and $y:\left\{2,4,6,8,10\right\}$.

$y^2-5y-11=13$

Short answer

Solution of the equation $y^2-5y-11=13$is$y=8.$

Step-by-step solution

Step 1. Given information.

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.

Step 2. Apply concept.

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.

Step 3. Calculation.

Substitute $y=2$in the given equation.

$2^2-5\times 2-11=13$

$\Rightarrow 4-10-11=13$

$\Rightarrow -17\ne 13$

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

Substitute $y=4$in the given equation.

$4^2-5\times 4-11=13$

$\Rightarrow 16-20-11=13$

$\Rightarrow -15\ne 13$

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

Substitute $y=6$in the given equation.

$6^2-5\times 6-11=13$

$\Rightarrow 36-30-11=13$

$\Rightarrow -5\ne 13$

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

Substitute $y=8$in the given equation.

$8^2-5\times 8-11=13$

$\Rightarrow 64-40-11=13$

$\Rightarrow 13=13$

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

Substitute $y=10$in the given equation.

${10}^2-5\times 10-11=13$

$\Rightarrow 100-50-11=13$

$\Rightarrow 39\ne 13$

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