Question

x/a - y/b=0 ax+by=a2+b2 by elimination method

Answer 1

Answer:

$x = a, \: y = b$

Step-by-step explanation:

$Given \: pair \: of \: Linear \\equations:$

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

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

/* 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

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

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

$\implies x = a$

$Put \: x = a \: in \: equation \\(1),\: we \: get$

$ab-ay = 0$

$\implies b-y = 0$

$\implies y = b$

Therefore,.

$x = a, \: y = b$

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Answer 2

Answer:

x=a, y =b

given pair of linear equations:

x/a – y/b=0

bx – ay/ ab=0

bx–ay=0 (equation 1)

and ax+by=a square+b square (equation 2)

multiply equation 1 by b, equation 2 by a, we get

b square x– any=0 (equation 3)

a squarex + aby = a ( a square+b square) (equation 4)

add equation 3 and 4,we get

x(a square +b square) =a(a square + b square)

x=a(a square+ b square) / (a square +b square)

x=a

put x=a in equation 1 , we get

ab–ay=0

b–y=0

y=b

therefore x=a and y= b