Question

ax + by = c
bx + ay = (1 + c)
solve by elimination method​

Answer 1

Step-by-step explanation:

Multiply 1 by b and 2 by a

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

Subtract

$(a {}^{2} - b {}^{2} )y = a + c(a - b) \\ \\ \\ y = \frac{ a + c(a - b)}{a {}^{2} - b {}^{2} }$

Similarly doing this by multiplying 1 by a and 2 by b

$\\ x = \frac{c(a - b) - b}{a {}^{2} - b {}^{2} }$

Answer 2

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

ax+by = c

∴a²x+aby = ac → (1)

bx+ay = 1+c

∴b²x+aby = b+bc → (2)

Subtracting (1)&(2);

(a²-b²)x = (a-b)c-b → (3)

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

Similarity, we get

abx+b²y = bc → (4)

abx+a²y = a+ac → (5)

Subtracting (4) from (5) we get;

(a²-b²)y = a+ac-bc

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

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