Question

Solve each equation.

$\left[\begin{array}{cc}4x-3& 3y\\ 7& 13\end{array}\right]\mathbf{=}\left[\begin{array}{cc}9& -15\\ 7& 2z+1\end{array}\right]$

Short answer

The solution is $\left(3,-5,6\right)$.

Step-by-step solution

– Description of step.

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

$\begin{array}{c}4x-3=9\\ 3y=-15\\ 13=2z+1\end{array}$

– Description of step.

Add 3 on both the sides of $4x-3=9$ and simplify.

$\begin{array}{c}4x-3+3=9+3\\ 4x=12\end{array}$

– Description of step.

Divide each side of $4x=12$by 4 to find the value of $x$.

$\begin{array}{c}\frac{4x}{4}=\frac{12}{4}\\ x=3\end{array}$

– Description of step.

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

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

– Description of step.

Subtract $1$ from both the sides of $13=2z+1$ and simplify.

$\begin{array}{c}13-1=2z+1-1\\ 12=2z\end{array}$

– Description of step.

Divide each side of $12=2z$by 2 to find the value of z.

$\begin{array}{c}\frac{12}{2}=\frac{2z}{2}\\ z=6\end{array}$

Therefore, the solution is $\left(3,-5,6\right)$.