Question

Solve the following simultaneous linear equations:

$33x+32y=34;32x+33y=31$

• A. $x=2$, $y=-1$
• B. $x=-1$, $y=2$
• C. $x=2$, $y=1$
• D. $x=1$, $y=2$

Answer 1

The correct option is A $x=2$, $y=-1$

The given equations are
$33x+32y=34$ ...(i)
$32x+33y=31$ ...(ii)
On adding (i) and (ii), we get
$65x+65y=65$

$\therefore x+y=1$ ...(iii)

On subtracting (ii) from (i), we get
$x-y=3$ ...(iv)
On adding (iii) and (iv)

$x+y=1$

$\underset{–}{x-y=3}$

$2x=4$
$\Rightarrow x=2$
On putting $x=2$ in (iii), we get
$2+y=1\Rightarrow y=1-2\Rightarrow y=-1$
$\therefore x=2,y=-1$