Solve this literal simultaneous equation for x and y. ax+by=c bx+ay=c

Question

Solve this literal simultaneous equation for x and y.


`ax+by=c`

`bx+ay=c`

Answer 1

The answer is below

Explanation:

Firstly, let us find the value of x. Multiply the first equation by a and the second equation by b to get:

a²x + aby = ca (3)

b²x + aby = cb (4)

Subtract equation 4 from equation 3 to get:

x(a² - b²) = c(a - b)

but a² - b² = (a + b)(a - b)

x(a + b)(a - b) = c(a - b)

x(a + b) = c

`x=(c)/(a+b)`

Secondly, let us find the value of y. Multiply the first equation by b and the second equation by a to get:

abx + b²y = cb (5)

abx + a²y = ca (6)

Subtract equation 5 from equation 6 to get:

y(a² - b²) = c(a - b)

but a² - b² = (a + b)(a - b)

y(a + b)(a - b) = c(a - b)

y(a + b) = c

`y=(c)/(a+b)`