Question

Solve the following equations:
$12x+8y-11z=-3$
$11x-13y-z=2$
$8x+17y-12z=-2$

• A. $x=6,y=2,andz=5$
  
• B. $x=3,y=2,andz=5$
  
• C. $x=3,y=2,andz=0$
  
• D. $x=3,y=4,andz=5$
  

Answer 1

The correct option is B $x=3,y=2,andz=5$


We have
$12x+8y-11z=-3$...........(1)
$11x-13y-z=2$............(2)
$8x+17y-12z=-2$...........(3)

Multiplying equation (2) by '-11', we get

$-121x+143y+11z=-22$...............(4)
also, $12x+8y-11z=-3$...........(1)

Adding equations (4) and (1), we get

$-109x+151y=-25$............(5)

Again, multiplying (2) by '-12', we have

$-132x+156y+12z=-24$...............(6)
also, $8x+17y-12z=-2$...........(3)

Adding equations (6) and (3), we get

$-124x+173y=-26$............(7)

Equations (5) and (7) can be rewritten as:

$-109x+151y+25=0$............(8)
$-124x+173y+26=0$............(9)

Therefore, by cross multiplication, we have

$\frac{x}{3926-4325}=\frac{y}{-3100+2834}=\frac{1}{-18857+18724}$

$\Rightarrow \frac{x}{-399}=\frac{y}{-266}=\frac{1}{-133}$

$\Rightarrow x=\frac{-399}{-133},z=\frac{-266}{-133}$

$\Rightarrow x=3,y=2$

Putting $x=3andy=2$ in equation (1), we get

$36+16-11z=-3$

$\Rightarrow 11z=55$

$\Rightarrow z=5$

Thus, we have $x=3,y=2,andz=5$