Q23. - Algebra 2

Question

Solve each equation.

$\left[\begin{array}{c}4x\\ y-1\end{array}\right]\mathbf{=}\left[\begin{array}{c}11+3y\\ x\end{array}\right]$

Step-by-Step Solution

Answer

The solution is $\left(\mathbf{14}\mathbf{,}\mathbf{15}\right)$.

Step 1 – Description of step.

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

 $\begin{array}{c}4x=11+3y\\ y-1=x\end{array}$

Step 2 – Description of step.

Substitute $y-1$ for x into $4x=11+3y$ and simplify.

 $\begin{array}{c}4\left(y-1\right)=11+3y\\ 4y-4=11+3y\\ 4y-3y=11+4\\ y=15\end{array}$

Step 3 – Description of step.

Substitute $15$ for y into $y-1=x$ and simplify to find the value of x.

$\begin{array}{c}y-1=x\\ 15-1=x\\ 14=x\end{array}$

Therefore, the solution is $\left(14,15\right)$.