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Method of Substitution to Find the Solution of a Pair of Linear Equations

Solve for x a...

Question

Solve for x and y:

$\frac{x}{a} + \frac{y}{b} = 2, a x - b y = a^{2} - b^{2} .$

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Solution

= 2 ---(1)
ax-by= ----(2)

x = 2a - $fraction numerator a y over denominator b end fraction$
substitute x in (2).
a(2a - $fraction numerator a y over denominator b end fraction$ ) - by =
$2 a squared minus fraction numerator a squared y over denominator b end fraction minus b y equals a squared minus b squared$
$a squared minus fraction numerator a squared y over denominator b end fraction minus b y plus b squared equals 0 a squared plus b squared equals fraction numerator a squared y over denominator b end fraction plus b y a squared plus b squared equals fraction numerator open parentheses a squared y plus b squared y close parentheses over denominator b end fraction b open parentheses a squared plus b squared close parentheses equals y open parentheses a squared plus b squared close parentheses$
therefore, y = b

x = a
therefore x=a

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