Question

Solve system of equations.

12.

$\begin{array}{l}2x-y=2\\ 3z=21\\ 4x+z=19\end{array}$

Short answer

The solution is $x=3,y=4,z=7.$

Step-by-step solution

Step-1 –Evaluating the value of z  from the second equation

Given system of equations are

$\begin{array}{l}2x-y+z=2\\ 3z=21\\ 4x+z=19\end{array}$

From second equation we get

$\begin{array}{l}3z=21\\ z=\frac{21}{3}\\ z=7\end{array}$

Step-2 –Evaluating the value of x from the third equation 

$\begin{array}{l}4x+z=19\\ 4x+7=19\\ 4x=19-7\\ 4x=12\\ x=3\end{array}$

Step-3–Evaluating the value of y from the first equation

$\begin{array}{l}2x-y=2\\ 2\left(3\right)-y=2\\ 6-y=2\\ -y=2-6\\ -y=-4\\ y=4\end{array}$