Question

Solve the following pair of linear (simultaneous) equations by the method of elimination:

$0.2x+0.1y=25$
$2(x-2)-1.6y=116$

• A. $x=50,y=-75$
• B. $x=-29,y=66$
• C. $x=100,y=50$
• D. $x=60,y=30$

Answer 1

Answer: (C)

$x=100,y=50$

$0.2x+0.1y=25$ ...$\left(1\right)$

$2x-1.6y=120$ ...$\left(2\right)$

Multiplying $\left(1\right)$ by $10$ and subtracting $\left(3\right)$ and $\left(2\right)$,

$2x+y=250$ ...$\left(3\right)$

$2x-1.6y=120$ ...$\left(2\right)$

$2.6y=130$

$y=50$

Substituting $y=50$ in $\left(1\right)$, we get

$0.2x+5=25$

$0.2x=20$

$x=100$

So,$x=100,y=50$

Option $C$