Question

Solve for x & y

Equation 1:
ax + by = r
ax + cy = s

Equation 2:
cx + ry = m
dx - sy = n

Answer 1

ax+by=r
-ax-cy=-s
------------------
by-cy=r-s

y(b-c)=r-s
y=r-s/(b-c)

Answer 2

What about X

Answer 3

let plug it in
ax+b(r-s)/(b-c)=r
just solve that

Answer 4

Better method of solving
\[\left( \begin{array}{cc} a & b \\ a & c \end{array} \right)\left( \begin{array}{c} x \\ y \end{array} \right)=\left( \begin{array}{c} r \\ s \end{array} \right)\]

Answer 5

c(ax + by = r )
-b(ax + cy = s)
------------------
acx + bcy = cr
-abx - bcy = -bs

-----------------
acx - abx = cr - bs

x(ac - ab) = cr - bs

x = cr - bs / ac - ab

Am I Right!

Answer 6

x y
\[\left\{\left\{\frac{b s-c r}{a (b-c)}\right\},\left\{\frac{r-s}{b-c}\right\}\right\}\]