Question

Use elimination method to solve the linear system Xi + 2x2-4x3-9 4. 2-x3-2

Answer 1

Adding equation (1) and twice the equation (2), we get

$x_{1}+10x_{1}+2x_{2}-2x_{2}-4x_{3}+4x_{3}=9+2\Rightarrow 11x_{1}=11\Rightarrow x_{1}=1$

equation (2) becomes as $5(1)-x_{2}+2x_{3}=1\Rightarrow -x_{2}+2x_{3}=-4$

Adding equation (2) and equation (3), we get

$-x_{2}+x_{2}+2x_{3}-x_{3}=-4+2\Rightarrow x_{3}=-2$

equation (3) becomes as $x_{2}-(-2)=2\Rightarrow x_{2}=2-2\Rightarrow x_{2}=0$

Therefore $x_{1}=1,$$x_{2}=0$ and $x_{3}=-2$