Giải thích các bước giải:

a.Ta có:

$\dfrac{x}8=\dfrac{y}{-7}=\dfrac{z}{12}=k$

$\to x=8k, y=-7k, z=12k$

Mà $-3x+10y-2z=236$

$\to -3\cdot 8k+10\cdot (-7k)-2\cdot 12k=236$ 

$\to -118k=236$

$\to k=-2$

$\to x=-16, y=14, z=-24$

b.Ta có:

$\dfrac{x-1}2=\dfrac{y-2}3=\dfrac{z-3}4=k$

$\to x=2k+1, y=3k+2, z=4k+3$

Mà $2x+3y-z=50$

$\to 2(2k+1)+3(3k+2)-(4k+3)=50$

$\to 9k+5=50$

$\to k=5$

$\to x=11, y=17, z=23$

c.Ta có:

$\dfrac{x-3}4=\dfrac{y}{15}\to x-3=\dfrac4{15}y\to x=\dfrac4{15}y+3$

$\dfrac{y}{10}=\dfrac{z+7}7\to z+7=\dfrac7{10}y\to z=\dfrac7{10}y-7$

Mà $3x-5z+2y=23$

$\to 3(\dfrac4{15}y+3)-5(\dfrac7{10}y-7)+2y=23$

$\to -\dfrac{7}{10}y+44=23$

$\to y=30$

$\to x=7, z=14$