Question

Solve each system of equations.

$\begin{array}{c}3x-3y=6\\ -6y=-30\\ 5z-2x=6\end{array}$

Short answer

The solution of given system of equation is $\left(\mathbf{7}\mathbf{,}\mathbf{5}\mathbf{,}\mathbf{4}\right)$.

Step-by-step solution

– Description of step.

Divide each side of $-6y=-30$ by $-6$.

$\begin{array}{c}\frac{-6y}{-6}=\frac{-30}{-6}\\ y=5\end{array}$

– Description of step.

Substitute 5 for $y$ into $3x-3y=6$ and simplify to obtain the value of $x$.

$\begin{array}{c}3x-3\left(5\right)=6\\ 3x-15=6\\ \frac{3x}{3}=\frac{21}{3}\\ x=7\end{array}$

– Description of step.

Substitute 7 for x into $5z-2x=6$ and simplify to obtain the value of $z$.

$\begin{array}{c}5z-2\left(7\right)=6\\ 5z-14=6\\ \frac{5z}{5}=\frac{20}{5}\\ z=4\end{array}$

Therefore, the solution of given system of equation is $\left(7,5,4\right)$.