Directions (Q.1-5): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
1) if x > y
2) if x < y
3) if x ≥ y
4) if x ≤ y
5) if x = y or relation cannot be established between 'x' and 'y'.
1. I. 8x+y=10
II. 4x+2y=13
2. I. (x+3) (y+2)=12
II. 2xy+4x+5y=11
3. I. (3x-2)/y = (3x+6)/(y+16)
II.(x+2)/(y+4) = (x+5)/(Y+10)
4. I. x^2+20x+4=50-25x
II. y^2-10y-24=0
5. I. (x^2-10x+16)/(x^2 -12x +24) = 2/3
II. y^2-y-20=0
Directions (Q.6-10): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
1) if x < y
2) if x > y
3) if x ≤ y
4) if x ≥ y
5) if x = y, or relationship between x and y can't be established.
6. I. 6x^2-49x+99=0
II. 5y^2+17y+14=0
7. I. 5x^2=19x-12
II. 5y^2+11y=12
8. I. x^3=(1331)^1/3
II. 2y^2-21y+55=0
9. I. 5x=7y+21
II. 11x+4y+109=0
10. I. 2x^2-11x+12=0
II. 2y^2-17y+36=0
Answers --
1. (2)
from both equation
x=7/12, y=16/3
y>x
2. (5)
xy+3y+2x +6 =12
2xy+6y+4x=12----(i)
2xy+5y+4x=11 ---- (ii)
From eq. (i) --- (ii)
Y = 1
From eq. (i)
x=1
x = y
3.(2)
(3x-2)/y = (3x+6)/(y+16)
48x-8y = 32 ---- (i)
(x+2)/(y+4) = (x+5)/(y+10)
y = 2x ---- (i)
From Equation (i) & (ii)
x=1, y=2
y>x
4.(5)
From the given Equation
x=1, -46
& y=-2,/2
x # y
5.(5)
From 1st equation
x^2-6x=0
x=0,6
From 2nd equation
(y+4) (y-5)
y=-4,5
x # y
6. (2)
6x^2-49x+99=0
(3x-11) (2x-9)=0
x=11/3, 9/2
5^2+17y+14=>
(5y+7) (y+2)=>
y=-2,-7/5
x>y
7.(4)
5x^2-19x+12=0
x=3,4/5
5y^2+11y=12
y = 4/5 ,-3
8. (2)
x=11
2y^2-21y+55= 0
(2y-11) (y-5)= 0
y=5,11/2
x>y
9. (2)
From given equation
x=-7
y=-8
x>Y
10 (3)
2x^2-11x+12=>
x=3/2,4
2y^2-17y+36=>
y=4,9/2
