Question

Solve ax+by=c, bx+ay=1+c

Answer 1

Answer:

$x =\frac{ac-b-bc}{a^{2}-b^{2}}$

$y = \frac{a+ac-bc}{a^{2}-b^{2}}$

Step-by-step explanation:

Given system of equations:

ax+by=c ---(1)

bx+ay=1+c ----(2)

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

a²x+aby=ac---(3)

b²x+aby=b+bc---(4)

Subtract (4) from (3) , we get

(a²-b²)x= ac-b-bc

$\implies x =\frac{ac-b-bc}{a^{2}-b^{2}}$

Now,

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

abx+b²y=bc---(5)

abx+a²y=a+ac---(6)

Subtract (5) from (6), we get

(a²-b²)y = a+ac-bc

$\implies y = \frac{a+ac-bc}{a^{2}-b^{2}}$

Therefore,

$x =\frac{ac-b-bc}{a^{2}-b^{2}}$

$y = \frac{a+ac-bc}{a^{2}-b^{2}}$

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