Question

Solve the following pairs of linear equations by elimination method:

$217x+131y=913$ and $131x+217y=827$

• A. $x=0,y=3$
• B. $x=-9,y=-4$
• C. $x=-8,y=-1$
• D. $x=3,y=2$

Answer 1

Answer: (D)

$x=3,y=2$

The equations are
$\Rightarrow 217x+131y=913$.....eq (1)
$\Rightarrow 131x+217y=827$.....eq (2)
Multiply $131$ in eq (1) and $217$ in eq (2)
$\Rightarrow 28427x+17161y=119603$... (3)
$\Rightarrow 28427x+47089y=179459$....(4)
Subtracting eq (3) and eq (,4)
$\Rightarrow 29928y=59856$

$\Rightarrow y=2$

Put the value of $y$ in eq (1)
$\Rightarrow 217x+131\times 2=913$

$\Rightarrow 217x=913-262$

$\Rightarrow x=3$
$\Rightarrow x=3$

Hence, option D is correct.