Solve: `a x+b y=c ,\ \ \ \ b x+a y=1+c`

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

Solve: a^2x+b^2y=c^2; b^2x+a^2y=d^2

Solve the following pair of linear equations: (i) p x+q y=p q ;" "q x p y=p+q (ii) a x+b y=c ;" "b x+a y=1+c (iii) x/a-y/b=0 ; a x+b y=a^2+b^2 (iv) (a-b)x+(a+b)y=a^2-2a b-b^2; (a+b)(x+y)=a^2+b^2 (v) 152 x 378 y= 74 ;" " 378

Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the equation |a x-b y-c b x-a y c x+a b x+a y-a x+b y-cc y+b c x+a c y+b-a x-b y+c|=0 represents a straight line.

If a + x = b + y = c + z + 1 , where a, b,c,x,y,z are non polar distinct real numbers , then |(x, a+y,x + a),(y , b+y , y + b),(z,c+y, z+c)| is equal to :

If x ,\ y , z are not all zero and if a x+b y+c z=0; b x+c y+a z=0; c x+a y+b z=0 Prove that x : y : z=1:1:1\ or\ 1:omega:omega^2or\ 1:omega^2:omegadot

The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a. |b x+a y c x+b y b^(prime)x+a ' y c^(prime)x+b ' y| b. |a x+b y b x+c y a^(prime)x+b ' y b ' x+c ' y| c. |b x+c y a x+b y b^(prime)x+c ' y a^(prime)x+b ' y| d. |a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|

If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent, then write the value of 2a b c-a b-b c-c adot

Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y