Question

Solve the following simultaneous equations. ax+by=5 and bx+ay=3. where a and b are constant.​

Answer 1

Step-by-step explanation:

ax+by = 5 …(1)

bx+ay = 3 … (2)

Multiply (1) by b and (2) by a to get

abx + b^2y = 5b … (3)

abx + a^2y = 3a … (4)

Subtract (3) from (4) to get

y(a^2-b^2) = 3a-5b, or

y = (3a-5b)/(a^2-b^2)

Multiply (1) by a and (2) by b to get

a^2x+aby = 5a …(5)

b^2x+aby = 3b … (6)

Subtract (6) from (5) to get

x(a^2-b^2) = 5a-3b, or

x = (5a-3b)/(a^2-b^2)