Question

Use elimination method for solving the following equations:
$100x+200y=700$, $200x+100y=800$

Answer 1

Given equations are

$100x+200y=700$ ....$\left(1\right)$

And $200x+100y=800$ ....$\left(2\right)$

Multiply equation equation $\left(2\right)$ by $2$, we get

$400x+200y=1600$ ....$\left(3\right)$

Subtract equation $\left(1\right)$ from $\left(3\right)$ to eliminate $y$,

$300x=900$

$\Rightarrow x=3$

Substitute this value of $x$ in equation $\left(1\right),$ we get

$100\left(3\right)+200y=700$

$\Rightarrow 300+200y=700$

$\Rightarrow 200y=400$

$\Rightarrow y=2$

Therefore, the solution is $x=3,y=2$.