Show that `y=2` is the root of `y-3=2y-5` and
`x=8` is the root of `1/2x+7=11`

If x_1, y_1 are the roots of x^2 +8x-97=0, x_2, y_2 are the roots of 4x^2 +32x-997=0 and x_3, y_3 are the roots of 9x^2 + 72x-9997=0 . Then the point (x_1, y_1), (x_2, y_2) and (x_3, y_3)

If 3x+5y=15 and x-2y=10 , what is the value of 2x+7y ?

Show that (1, 2) lies on the locus x^(2)+y^(2)-4x-6y+11=0 .

Show that the distance of the centre of the circle x^2+y^2=2x from the common chord of the circles x^2+y^2+5x-8y+1=0 and x^2+y^2-3x+7y-25=0 is 2.

Show that the tangents to the curve y=7x^3+11 at the points where x = 2 and x = -2 are parallel.

Show that x=2,\ \ y=1 is not a solution of the system of simultaneous linear equations: 2x+7y=11 ;\ \ \ x-3y=5

If the ratio between 8 and 11 is the same as the ratio of 2x - y to x + 2y , find the value of (7x)/(9y) .

Statement -1 : If x is real and y = (x^(2) -x+3)/(x+2) , " then " y in (-oo,oo) - (-11,1) Statement -2 : If [] represents the greatest integer function and f(x) =x -[x] then number of real roots of the equation f(x) +f (1/x)=1 are infinite. Statement -3 : if the difference of the roots of the equation x^(2)+hx +7=0 is 6, then , possible value (s) of h are -8 and 8.

Show that the planes 2x+6y-6z=7\ a n d\ 3x+4y+5z=8 are at right angles.

Show that the following system of equation is inconsistent. 2x-y+3z=5,3x+2y-z=7,4x+5y-5z=0