Q18. - Algebra 2

Question

Solve each equation.

$\left[\begin{array}{c}4x\\ 5\end{array}\right]\mathbf{=}\left[\begin{array}{c}15+x\\ 2y-1\end{array}\right]$

Step-by-Step Solution

Answer

The solution is $\left(\mathbf{5}\mathbf{,}\mathbf{3}\right)$.

Step 1 – Description of step.

As the matrices are equal, the corresponding elements are equal. Write the two linear equations to show this equality.

 $\begin{array}{c}4x=15+x\\ 5=2y-1\end{array}$

Step 2 – Description of step.

Add 1 on both the sides of $5=2y-1$ and simplify.

$\begin{array}{c}5+1=2y-1+1\\ 6=2y\end{array}$

Step 3 – Description of step.

Divide each side of $6=2y$ by 2 to find the value of $y$.

$\begin{array}{c}\frac{6}{2}=\frac{2y}{2}\\ 3=y\end{array}$

Step 4 – Description of step.

Subtract $x$ from both the sides of $4x=15+x$ and simplify.

$\begin{array}{c}4x-x=15+x-x\\ 3x=15\end{array}$

Step 5 – Description of step.

Divide each side of $3x=15$ by 3 to find the value of $x$.

$\begin{array}{c}\frac{3x}{3}=\frac{15}{3}\\ x=5\end{array}$

Therefore, the solution is $\left(5,3\right)$.