Match each step with step-by-step description of how you would solve the system. $$\left( \begin{array} { c }
2 x - y + 3 z = 24 \
x - 2 y - z = 1 \
3 x + 5 y + 8 z = 47
\end{array} \right)$$
-Finding x , y , z . x = 4, y = -1 , z = 5.
A) 1st step
B) 2nd step

Question

Match each step with step-by-step description of how you would solve the system. $$\left( \begin{array} { c } 
2 x - y + 3 z = 24 \
x - 2 y - z = 1 \
3 x + 5 y + 8 z = 47
\end{array} \right)$$
-Finding x , y , z . x = 4, y = -1 , z = 5.
A) 1st step
B) 2nd step

Quizplus · Accepted Answer

1st step: We can use elimination method to get rid of the variable y. Adding 2 times the second equation to the first equation, we get 
$$4x + 5z = 26$$
2nd step: Now we can use substitution method to solve for x and z. From the third equation, we have 
$$y = \frac{47 - 3x - 8z}{5}$$
Substitute this into the second equation, we get 
$$x - 2\left(\frac{47 - 3x - 8z}{5}ight) - z = 1$$
Simplifying this equation, we get 
$$23x + 6z = 127$$
Solving the system of two equations in two variables, 
\begin{align*}
4x + 5z &= 26 \
23x + 6z &= 127
\end{align*}
we get $x = 4, z = 5$. Substitute these values back into any of the three original equations, we get $y = -1$. Therefore, the solution is $(x, y, z) = (4, -1, 5)$.

Match Each Step with Step-By-Step Description of How You Would (2x−y+3z=24x−2y−z=13x+5y+8z=47)\left( \begin{array} { c } 2 x - y + 3 z = 24 \\x - 2 y - z = 1 \\3 x + 5 y + 8 z = 47\end{array} \right)​2x−y+3z=24x−2y−z=13x+5y+8z=47​​

Match Each Step with Step-By-Step Description of How You Would $\left( \begin{array} { c } 2 x - y + 3 z = 24 \\x - 2 y - z = 1 \\3 x + 5 y + 8 z = 47\end{array} \right)$