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Directions: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.

I.x^{2} +11x +18 = 0

II.y^{2} +16y+ 48 = 0

2.

I.3x^{2} +10x +7 = 0

II.3y^{2} +4y+ 1 = 0

3.

I.5x^{2} -7x +2 = 0

II.2y^{2} -7y+ 3 = 0

4.

I.2x^{2} -3x +1 = 0

II.y^{2}-8 y+ 15 = 0

5.

I)x = (-4)^{2}

II)y^{2}=256

Directions:6-10):**Two equations (I) and (II) are given in each question. On the basis of these questions, you have to decide the relation between p and q and give answer:**

6.

- 5p
^{2}– 87p + 378 = 0 - 3q
^{2}– 49q + 200 = 0

7.

- 10p
^{2}– p – 24 = 0 - q
^{2}– 2q = 0

8.

- p
^{2}– 5p + 6 = 0 - 2q
^{2}– 15q + 27 = 0

9.

- 3p + 2q = 301
- 7p – 5q = 74

10.

- 14p
^{2}– 37p + 24 = 0 - 28q
^{2}– 53q + 24 = 0

**Check your Answers below:**

Directions:1-5)

**In the given question two equations are given. You have to Solve both the equations and given answer.**##### 1. Question

I.x

^{2}+11x +18 = 0

II.y^{2}+16y+ 48 = 0Ans:5

I)x^{2}+11x +18 = 0

x^{2}+2x+9x+18=0

x(x+2)+9(x+2)=0

(x+2) (x+9)=0

x=-2,-9y^{2}+16 y+ 48 = 0

y^{2}+4y+12y+48=0

y(y+4) + 12(y+4)=0

(y+4)(y+12)=0

y=-4,-12

**So relationship between x and y cannot be established**##### 2. Question

I.3x

^{2}+10x +7 = 0

II.3y^{2}+4y+ 1 = 0Ans:4

I.3x^{2}+10x +7 = 0

3x^{2}+3x+7x+7=0

3x(x+1) + 7(x+1)=0

(x+1) (3x+7)=0

x=-1,-7/3II.3y^{2}+4y+ 1 = 0

3y^{2}+ 3y+y+1=0

3y(y+1) + 1(y+1) =0

(y+1) (3y+1)=0

y=-1,-1/3

**So x ≤ y**##### 3. Question

I.5x

^{2}-7x +2 = 0

II.2y^{2}-7y+ 3 = 0Ans:5

I.5x^{2}-7x +2 = 0

5x^{2}-5x-2x+2=0

5x(x-1) -2(x-1)=0

(x-1) (5x-2)=0

x=1,2/5II.2y^{2}-7 y+ 3 = 0

2y^{2}-6y-y+3=0

2y(y-3) -1(y-3)=0

(y-3) (2y-1)=0

y=3,1/2

**Relationship between x and y cannot be established**##### 4. Question

I.2x

^{2}-3x +1 = 0

II.y^{2}-8 y+ 15 = 0Ans:2

I.2x^{2}-3x +1 = 0

2x^{2}-2x-x +1=0

2x(x-1)-1(x-1)=0

(x-1) (2x-1)=0

x=1,1/2II.y^{2}-8 y+ 15 = 0

y^{2}-3y-5y+15=0

y(y-3)-5(y-3)=0

(y-3)(y-5)=0

y=3,5

**So x <y**##### 5. Question

I)x = (-4)

^{2}

II)y^{2}=256Ans:3

I)x = (-4)^{2}x=16II)y

^{2}=256y=16 and -16

**Hence x ≥ y**Directions:6-10):

**Two equations (I) and (II) are given in each question. On the basis of these questions, you have to decide the relation between p and q and give answer**##### 6. Question

- 5p
^{2}– 87p + 378 = 0 - 3q
^{2}– 49q + 200 = 0

Ans:1

I.5p^{2 }– 45p – 42p + 378 = 05p (p – 9) – 42(p- 9) = 0(5p – 42)(p -9) = 0

p = 9, 42/5 = 9, 8.4

II.3q

^{2 }– 24q – 25q + 200=03q (q – 8) -25(q – 8) = 0

(q – 8)(3q-25)=0

q = 8, 25/3 = 8, 8.33

Hence, p>q

- 5p
##### 7. Question

- 10p
^{2}– p – 24 = 0 - q
^{2}– 2q = 0

Ans:5

I.10p^{2 }+15p – 16p – 24 = 05p(2p + 3) – 8(2p+ 3)=0(2p + 3)(5p – 8) = 0

p = -3/2, 8/5 = -1.5, 1.6

II.q

^{2}– 2q = 0q(q -2) = 0

q = 0, 2

(i.e.) no relationship exists between p and q.

- 10p
##### 8. Question

- p
^{2}– 5p + 6 = 0 - 2q
^{2}– 15q + 27 = 0

Ans:4

p^{2}– 2p – 3p + 6 =0p(p -2) – 3(p -2) = 0(p -2) (p -3) = 0

p =2, 3

2q

^{2 }– 6q – 9q + 27 = 02q(q – 3)-9(q -3) = 0

(q- 3) (2q -9) = 0

q = 3, 9/2 = 3, 4.5

Hence, p ≤ q

- p
##### 9. Question

- 3p + 2q = 301
- 7p – 5q = 74

Ans:2

I.eqn (I) × 5 + eqn (II) × 2[15p + 10q = 1505] + [14p – 10q = 148] = 29p = 1653p = (1653/29) = 57

And q = 65

Hence, p< q

##### 10. Question

- 14p
^{2}– 37p + 24 = 0 - 28q
^{2}– 53q + 24 = 0

Ans:3

14p^{2}– 37p + 24 = 014p^{2 }– 21p- 16p + 24 = 07p(2p -3) -8(2p -3) = 0

(2p – 3)(7p – 8) = 0

p = (3/2), (8/7)

II.28q

^{2 }– 53q + 24 = 028q

^{2 }-21q – 32q + 24 =07q(4q – 3) -8(4q – 3) = 0

(7q – 8) (4q – 3) = 0

q = 8/7, 3/4

p ≥ q

- 14p