Q50. - Algebra 1

Question

Find the solution of each equation if the replacement sets are $x:\left\{1,3,5,7,9\right\}$ and $y:\left\{6,8,10,12,14\right\}$

$y-9=3$

Step-by-Step Solution

Answer

The solution of the equation $y-9=3$ is $y=12$.

Step 1. Given information.

We have an equation $y-9=3$ and a set $y:\left\{6,8,10,12,14\right\}$

To find the solution of the given equation at every value of $y$.

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 $y=6$ in the equation $y-9=3$

$$\begin{gathered} 6-9=3 \\ \Rightarrow -3\ne 3 \end{gathered}$$         

$y=6$ is not a solution

Substitute $y=8$ in the equation $y-9=3$

$$\begin{gathered} 8-9=3 \\ \Rightarrow -1\ne 3 \end{gathered}$$         

$y=8$ is not a solution

Substitute $y=10$ in the equation $y-9=3$

$$\begin{gathered} 10-9=3 \\ \Rightarrow 1\ne 3 \end{gathered}$$ 

$y=10$ is not solution

Substitute $y=12$ in the equation $y-9=3$

  $$\begin{gathered} 12-9=3 \\ \Rightarrow 3=3 \end{gathered}$$

$y=12$ is a solution

Substitute $y=14$ in the equation $y-9=3$

   $$\begin{gathered} 14-9=3 \\ \Rightarrow 5=3 \end{gathered}$$

Hence, the $y=12$ is the solution of the given equation.