Question

I. $7x+6y+4z=122$
II. $4x+5y+3z=88$
III. $9x+2y+z=78$

• A. $x<y=z$
• B. $x\le y<z$
• C. $x<y>z$
• D. $x=y>z$
• E. $x=y=z$ or none of the above relationship is established

Answer 1

The correct option is A $x<y=z$

$7x+6y+4z=122\dots \left(i\right)4x+5y+3z=88\dots \left(ii\right)9x+2y+z=78\dots \left(iii\right)$
By equation (iii) $\times$ 3 - equation (ii),
$27x+6y+3z=2344x+5y+3z=88\underset{–}{----}\left(iv\right)23x+y=146$
By equation (iii) $\times$ 4 - equation (i),
$36x+8y+4z=3127x+6y+4z=122\underset{–}{----}\dots \left(v\right)29x+2y=190$
By equation (iv) $\times$ 2-equation (v),
$46x+2y=29229x+2y=190\underset{–}{----}\left(iv\right)17x=102\Rightarrow x=6$
From equation (iv),
$23\times 3+y=146\Rightarrow y=146-138=8$
From equation (iii),
$9\times 6+2\times 8+z=78\Rightarrow 54+16-z=78\Rightarrow z=78-70=8$
clearly, $x<y=z$