Question

Solve by substitution method:- x/a - y/b=0 and ax+by=a^2+b^2

Answer 1

Answer:

x=a,y=b

Step-by-step explanation:

$$\begin{lgathered}Given \: pair \: of \: Linear \\equations:\end{lgathered}$$

$$\begin{lgathered}\frac{x}{a}-\frac{y}{b}=0\\\implies \frac{bx-ay}{ab}=0\\\implies bx-ay = 0 \:---(1)\end{lgathered}$$

$$and\: ax+by=a^{2}+b^{2}\:---(2)$$

/* multiply equation (1) by b, equation (2) by a, we get

$$b^{2}x-aby = 0 \:---(3)$$

$$a^{2}x+aby=a(a^{2}+b^{2})\:---(4)$$

/* Add equations (3) and (4),we get

$$x(a^{2}+b^{2})=a(a^{2}+b^{2})$$

$$\implies x = \frac{a(a^{2}+b^{2})}{(a^{2}+b^{2})}$$

$$\implies x = a$$

$$\begin{lgathered}Put \: x = a \: in \: equation \\(1),\: we \: get\end{lgathered}$$

$$ab-ay = 0$$

$$\implies b-y = 0$$

$$\implies y = b$$

Therefore,.

$$x = a, \: y = b$$

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