Q72. - Algebra 2

Question

Solve the following system of equations?

$\begin{array}{c}x+y=5\\ x+y+z=4\\ 2x-y+2z=-1\end{array}$

Step-by-Step Solution

Answer

The solution for the system of equations is$x=2,y=3,z=-1$  .

Step 1. Write down the given information.

The given system of equations are,

$\begin{array}{c}x+y=\mathrm{5....}\left(1\right)\\ x+y+z=\mathrm{4....}\left(2\right)\\ 2x-y+2z=-\mathrm{1....}\left(3\right)\end{array}$

Step 2. Calculation.

From (1) plugging $x+y=5$  in (2) gives,

Plugging $z=-1$  in (3),

$\begin{array}{c}2x-y+2z=-\mathrm{1....}\left(\text{From }\left(3\right)\right)\\ 2x-y+2(-1)=-\mathrm{1....}(\text{Plugging }z=-1)\\ 2x-y-2=-1\\ 2x-y=\mathrm{1....}\left(4\right)\end{array}$

Adding (1) and (4) gives,

 $\begin{array}{c}3x=6\\ x=2\end{array}$

Plugging $x=2$  in (1) gives,  .

Step 3. Conclusion.

The solution for the system of equations is $x=2,y=3,z=-1$ .