Using Cramer's rule to solve for y in 2×2 and 3×3 systems

[tatianaiistb]

Homework Statement

Use Cramer's rule to solve for y (only). Call the 3x3 determinant D:

(a) ax+by = 1
cx+dy=0

(b) ax+by+cz=1
dx+ey+fz=0
gx+hy+iz=0

Homework Equations

Cramer's Rule: x=A^-1*b

The Attempt at a Solution

(a) So far I have,

y= [det [a 1; c 0] / det [a b; c d]} = (0-c)/(ad-bc)=-c/(ad-bc)

I don't know how to proceed...

Same with part (b),

y= [det[a 1 c; d 0 f; g o i]/det[a b c; d e f; g h i]] = (fg-di)/(aei+bfg+cdh-ceg-afh-ibd)

Is there a way to simplify this?

 

[vela]

You're done.