Question

Solve: $99x+101y=499,101x+99y=501$

Answer 1

Step 1: Adding both the equations.

Given that $99x+101y=499\dots \left(1\right)$

$101x+99y=501\dots \left(2\right)$

Adding equations $\left(1\right)$ and $\left(2\right)$, we get.

$200x+200y=1000$

$\Rightarrow$ $x+y=5\dots \left(3\right)$

Step 2: Subtracting one equation from another equation.

Subtracting $\left(1\right)$from $\left(2\right)$, we get,

$\Rightarrow$$2x–2y=2$

$\Rightarrow$ $x–y=1\dots \left(4\right)$

Step 3: Find the value of $x$ and $y$

Adding $\left(3\right)$ and $\left(4\right)$, we get,

$$\begin{gathered} 2x=6 \\ x=3 \end{gathered}$$

Putting the value of $x$in $\left(3\right)$,

we get, $y=2$

Hence, $x=3$ and $y=2$ is the correct answer.