Question

Solve system of equations.

$\begin{array}{l}-4a=8\\ 5a+2c=0\\ 7b+3c=22\end{array}$

Short answer

The solution is $a=-2,b=1,c=5$

Step-by-step solution

Step-1 –Evaluating the value of \[a\]  from the second equation

Given system of equations are

$\begin{array}{l}-4a=8\\ 5a+2c=0\\ 7b+3c=22\end{array}$

From the first equation we get

$\begin{array}{l}-4a=8\\ a=-2\end{array}$

Step-2 –Evaluating the value of c from the second equation 

$\begin{array}{l}5a+2c=0\\ 5(-2)+2c=0\\ -10+2c=0\\ 2c=10\\ c=5\end{array}$

Step-3–Evaluating the value of b from the third equation

$\begin{array}{l}7b+3c=22\\ 7b+3\left(5\right)=22\\ 7b=22-15\\ 7b=7\\ b=1\end{array}$