QUESTION: x+ay=b and cx+dy=f. Solve for x and y when a,b,c,d,f are constants.
The equations are.
x+ay=b -------- (1)
cx+dy=f. -------- (2)
Multiply (1) by c.
cx+acy=bc ----- (3)
cx+dy=f. ------- (4)
subtract (4) from (3).
acy - dy = bc - f
y(ac - d) = bc - f
y = (bc - f)/(ac - d)
From (1), x = b - ay
Substituting for y = (bc - f)/(ac - d),
x = b - a(bc - f)/(ac - d) = (abc - bd - abc + af)/(ac - d) = (af - bd)/(ac - d)
x = (af - bd)/(ac - d)