Question

Solve for $xandy$

$x+y=a-b;ax-by=a^2+b^2$

Answer 1

Step 1:Simplification to make the$\text{'}y\text{'}$ coefficient as same

$$\begin{gathered} x+y=a-b...................................\left(1\right) \\ ax-by=a^2+b^2...............................\left(2\right) \end{gathered}$$

Equation (1) $\times b$

$$\begin{gathered} Equation\left(1\right)\Rightarrow bx+by=ab-b^2.................................\left(3\right) \\ Equation\left(2\right)\Rightarrow ax-by=a^2+b^2..........................................\left(2\right) \end{gathered}$$

Step 2: Applying elimination method to find the value of $\mathit{x}$

$$\begin{gathered} equation\left(2\right)+\left(3\right) \\ \Rightarrow ax+bx=a^2+ab \\ \Rightarrow x(a+b)=a(a+b) \\ \Rightarrow x=\frac{a(a+b)}{a+b} \\ \Rightarrow x=a \end{gathered}$$

Step 3:Finding the value of $\mathbf{\text{'}}\mathit{y}\mathbf{\text{'}}$by substitution method

$$\begin{gathered} Substitutethevalueofx=ainequation\left(1\right) \\ Equation\left(1\right)\Rightarrow a+y=a-b \\ \Rightarrow y=a-b-a \\ \Rightarrow y=-b \end{gathered}$$

Therefore the values of$x=aandy=-b$