Question

Solve the following system of linear equations.x + 3y + z = - 42x – 4y – 3z = 73x – 3y + 4z = 13AnswerBH」KeyboardX =y =z =

Answer 1

Given

Solve the following system of linear equations.

x + 3y + z = - 4

2x – 4y – 3z = 7

3x – 3y + 4z = 13

Solution

$\begin{bmatrix}x+3y+z=-4 \\ 2x-4y-3z=7 \\ 3x-3y+4z=13\end{bmatrix}$

Substitute x= -4-3y-z

$\begin{bmatrix}2\mleft(-4-3y-z\mright)-4y-3z=7 \\ 3\mleft(-4-3y-z\mright)-3y+4z=13\end{bmatrix}$

Simplify

$\begin{bmatrix}-10y-5z-8=7 \\ -12y+z-12=13\end{bmatrix}$

Make y the subject

$\begin{gathered} -10y-5z-8=7 \\ -10y\text{ -5z=7+8} \\ -10y-5z=15 \\ \text{divide all through by 5} \\ -2y-z=3 \\ y=-\frac{z+3}{2} \end{gathered}$

Now substitute

$\begin{bmatrix}-12\mleft(-\frac{z+3}{2}\mright)+z-12=13\end{bmatrix}$

Simplify

$\begin{gathered} \\ \begin{bmatrix}7z+6=13\end{bmatrix} \\ \text{Make z the subject} \\ 7z=13-6 \\ 7z=7 \\ \text{divide both sides by 7} \\ \frac{7z}{7}=\frac{7}{7} \\ z=1 \end{gathered}$

Now substitute z=1

$\begin{gathered} y=-\frac{z+3}{2} \\ y=-\frac{1+3}{2}=-\frac{4}{2}=-2 \end{gathered}$

Finally, to find x

when z =1 and y =-2

$\begin{gathered} x+3y+z=-4 \\ x+3(-2)+1=-4 \\ x-6+1=-4 \\ \text{collect the like terms} \\ x-5=-4 \\ x=-4+5 \\ x=1 \end{gathered}$

The final answer

$\begin{gathered} x=1 \\ y=-2 \\ z=1 \end{gathered}$