Question

15. Solve the following system of equations in x and y:
ax + by = C,
bx + ay = 1+c.​

Answer 1

Answer:

$given \: equatios \: are \: \\ ax + by = c \: \: \: \: \: \: \: \: \: \: \: \: \: \: - -- - - (1) \\ bx + ay = 1 + c \: \: \: \: \: \: \: - - - - (2)$

$eq(1) \times b = > abx + {b}^{2} y = bc \: \: \: \: \: \: \: \: \: \: - - - - (3) \\ eq(2) \times a = > abx + {a}^{2} y = a(1 + c) \: \: \: \: \: \: \: \: \: - - - - (4)$

$eq(3) - eq(4) = > \\ ( {b}^{2} - {a}^{2} )y = bc - a - ac \\ y = \frac{bc - a - ac}{ {b}^{2} - {a}^{2} }$

$by \: eq(1) = > \\ ax + b( \frac{bc - a - ac}{ {b}^{2} - {a}^{2} } ) = c \\ ax = c - b( \frac{bc - a - ac}{ {b}^{2} - {a}^{2} } ) \: \\ x = \frac{1}{a}( c - b( \frac{bc - a - ac}{ {b}^{2} - {a}^{2} } ) \: )$

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