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-20=0,x_(2),y_(2), are the roots of 4x^(2)+32x-57=0 and x_(3),y_(3), are the roots of 9x^(2)+72x-112=0, then the points,(x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) -

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))

Show that x = 3 , y = 2 is not a solution of the system of linear equations 3x - 2y = 5, 2 x + y = 7

Find the solution of x + y = 7 and 2x - 3y = 11 .

Verify by substitution that the root of . (i) 3x-5=7 is x=4 . (ii) 3+2x=9 is x=3 . (iii) 5x-8=2x-2 is x=2 . (iv) 8-7y=1 is y=1 . (v) (z)/(7)=8 is z=56 .

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

Show that the following set of curves intersect orthogonally: y=x^(3) and 6y=7-x^(2)x^(3)-3xy^(2)=-2 and 3x^(2)y-y=2x^(2)+4y^(2)=8 and x^(2)-2y^(2)=4

Show that the lines 2x + 3y - 8 = 0 , x - 5y + 9 = 0 and 3x + 4y - 11 = 0 are concurrent.

Two point B(x_(1), y_(1)) and C(x_(2), y_(2)) are such that x_(1), x_(2) are the roots of the equation x^(2)+4x+3=0 and y_(1),y_(2) are the roots of the equation y^(2)-y-6=0 . Also x_(1)lt x_(2) and y_(1)gt y_(2) . Coordinates of a third point A are (3, -5). If t is the length of the bisector of the angle BAC, then l^(2) is equal to.

(i) x+2y=-7 and 3x-2y=-1, then find the value of x. (ii) If x+y=8 and 4y-x=2, then find the value of y. (iii) If 3x+5y=9 and 5x+3y=7, then find the value of x+y. (iv) If 3x-y=11 and x-3y=17, then find the value of x-y.