Question

Solve the simultaneous equations using the convergent iterations:
$5x$ + $y$ + $2z$ = $19$
$2x$ + $3y$ +$8z$ = $39$
$x$ + $4y$ -$2z$ = $-2$

• A. $x=2$, $y=2$ and $\text{z}=1$
• B. $x=2$, $y=1$ and $\text{z}=4$
• C. $x=3$, $y=2$ and $\text{z}=2$
• D. None of these

Answer 1

Answer: (B)

$x=2$, $y=1$ and $\text{z}=4$

$5x+y+2z=19$

$x+4y-2z=-2$

Adding above two equations we get,

$5x+y+2z+x+4y-2z=19-2$

$⟹6x+5y=17$

Taking another equation

$2x+3y+8z=39$

Multiplying the given last equation with $4$

$4x+16y-8z=-8$

Adding above two equations

$2x+3y+8z+4x+16y-8z=31$

$⟹6x+19y=31$

Now,

$6x+19y-(6x+5y)=31-17$

$⟹19y-5y=14$

$⟹y=1$

By substituting the value of $y$ into the above equations

we get,

$x=2$ and $z=4$

$\therefore x=2,y=1$ and $z=4$.