Respuesta :
X=-1
Y=1
Z=1
Explanation
[tex]\begin{gathered} 5x-3y+4z=-4\Rightarrow equation(1) \\ -4x+2y-3z=3\Rightarrow equation(2) \\ -x+5y+7z=13\Rightarrow equation(3) \end{gathered}[/tex]Step 1
in order to eliminate y,
a))Mutiipy equation (3) by 5, then add the new equation to equation (1)
[tex]\begin{gathered} -x+5y+7z=13\text{ }\Rightarrow eq(3)\text{ by 3} \\ 5x-3y+4z=-4\text{ }\Rightarrow eq(3)\text{ by 5} \\ \text{so} \\ -3x+15y+21z=39 \\ 25x-15y+20z=-20 \\ _{-------------------} \\ 22x+41z=19\Rightarrow equation(4) \end{gathered}[/tex]so
now, equation(1) by 2, added to equaiton (2) by 3
[tex]\begin{gathered} 5x-3y+4z=-4\Rightarrow equation(1)\cdot2 \\ -4x+2y-3z=3\Rightarrow equation(2)\cdot3 \\ so \\ 10x-6y+8z=-8 \\ -12x+6y-9z=9 \\ _{-----------------} \\ -2x-z=1\Rightarrow equation\text{ (5)} \end{gathered}[/tex]Step 2
now, use equation(4) and equation (5) to find x and z
[tex]\begin{gathered} 22x+41z=19\Rightarrow equation(4) \\ -2x-z=1\Rightarrow equation\text{ (5)} \end{gathered}[/tex]a)in order to eliminate x, multiply equation (5) by 11, then add the result to equation(4)
[tex]\begin{gathered} -2x-z=1\Rightarrow equation\text{ (5) by 11} \\ -22x-11z=11 \\ ad\text{d to equation(4)} \\ -22x-11z=11 \\ 22x+41z=19 \\ ------------ \\ 30z=30 \\ so \\ z=\frac{30}{30}=1 \\ z=1 \end{gathered}[/tex]hence
Z= 1
Step 3
now, replace the z value into equation(5) and isolate x
[tex]\begin{gathered} -2x-z=1\Rightarrow equation\text{ (5)} \\ \text{replace} \\ -2x-(1)=1 \\ -2x-1=1 \\ add\text{ 1 in both sides} \\ -2x-1+1=1+1 \\ -2x=2 \\ \text{divide both sides by -2} \\ \frac{-2x}{-2}=\frac{2}{-2} \\ x=-1 \end{gathered}[/tex]so
X=1
Step 4
finally, replace X and Z value into equation (1), then solve for x
[tex]\begin{gathered} 5x-3y+4z=-4\Rightarrow equation(1) \\ 5(-1)-3y+4(1)=-4 \\ -5-3y+4=-4 \\ \text{add like terms} \\ -3y-1=-4 \\ \text{add 1 in both sides} \\ -3y-1+1=-4+1 \\ -3y=-3 \\ y=\frac{-3}{-3} \\ y=1 \end{gathered}[/tex]therefore,
Y=1
so, the answer is
X=-1
Y=1
Z=1
I hope this helps you
