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Directions:1-10) **In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:**

1.

I. 8x^{2} – 49x + 45 = 0

II. 8y^{2} – y – 9 = 0

2.

I. 42x – 17y = -67

II. 7x + 12y = -26

3.

I .x^{2} – 8x + 15 = 0

II. 2y^{2} – 21y + 55 = 0

4.

I. x^{2} + 12x + 32 = 0

II. 2y^{2} + 15y + 27 = 0

5.

I. 6x^{2} – 17x + 12 = 0

II. 7y^{2} – 13y + 6 = 0

6.

I.11x + 5y = 117

II.7x + 13y = 153

7.

I.6x^{2} + 51x + 105 = 0

II.2y^{2} + 25y + 78 = 0

8.

I.6x + 7y = 52

II.14x + 4y = 35

9.

I.x^{2} + 11x + 30 = 0

II.y^{2} + 12y + 36 = 0

10.

I.2x^{2} + x – 1 = 0

II.2y^{2} – 3y + l = 0

**Check your Answers below:**

Directions:1-10) **In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:**

##### 1. Question

I. 8x^{2} – 49x + 45 = 0

II. 8y^{2} – y – 9 = 0

8x

^{2}– 49x + 45 = 0

8x^{2}-40x-9x+45=0

8x(x-5) – 9 (x-5) =0

(8x-9) (x-5) =0

X =9/8, 5

8y^{2} – y – 9 = 0

8y^{2}+8y-9y-9=0

8y(y+1) -9 (y+1) =0

(8y-9) (y-+1) = 0

Y= 9/8,-1

X≥ Y

##### 2. Question

I. 42x – 17y = -67

II. 7x + 12y = -26

42x – 17y = -67 ——- 1

7x + 12y = -26 ——– 2

X = -2 Y= -1

X<Y

##### 3. Question

I .x^{2} – 8x + 15 = 0

II. 2y^{2} – 21y + 55 = 0

x

^{2}– 8x + 15 = 0

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

x(x-5) -3 (x-5) =0

(x-3) (x-5) =0

X =5, 3

2y^{2} – 21y + 55 = 0

2y^{2}-10y-11y+55 = 0

2y (y-5) -11 (y-5) =0

(2y-11) (y-5) =0

Y =5, 11/2

x ≤ y

##### 4. Question

I. x^{2} + 12x + 32 = 0

II. 2y^{2} + 15y + 27 = 0

x

^{2}+ 12x + 32 = 0

x^{2}+8x+4x+32=0

x(x+8) + 4 (x+8) =0

(x+4) (x+8) =0

X =-4,-8

2y^{2} + 15y + 27 = 0

2y^{2}+6y+9y+27 =0

2y (y+3) +9 (y+3) =0

(2y+9) (y+3) =0

Y = -9/2 ,-6/2 =-4.5,-3

x = y or relation cannot be established

##### 5. Question

I. 6x^{2} – 17x + 12 = 0

II. 7y^{2} – 13y + 6 = 0

6x

^{2}– 17x + 12 = 0

6x^{2}-9x-8x+12=0

3x (2x-3) – 4 (2x-3) =0

(3x-4) (2x-3) =0

X =3/2, 4/3

7y^{2} – 13y + 6 = 0

7y^{2}-7y -6y+6 =0

7y (y-1) -6 (y-1) =0

(7y-6) (y-1) =0

Y =6/7, 1

X>Y

##### 6. Question

I.11x + 5y = 117

II.7x + 13y = 153

eqn (I) × 7

77x + 35y = 819 —(III)

eqn (II) × 11

77x + 143y = 1683——(IV)

On solving (III) & (IV) we get,

– 108y = – 864

y = 8, x = 7 i.e., x < y

##### 7. Question

I.6x^{2} + 51x + 105 = 0

II.2y^{2} + 25y + 78 = 0

6x

^{2}+ 21x + 30x + 105 = 0

x = -5, – 7/2

2y^{2} + 12y + 13y + 78 = 0

y =-13/2, – 6

x > y

##### 8. Question

I.6x + 7y = 52

II.14x + 4y = 35

Eqn (I) × 4

Eqn (II) × 7

24x + 28y = 208 —- (III)

98x + 28y = 245 —— (IV)

On solving (III) & (IV) we get,

– 74x = – 37

x =1/2, y = 7

x < y

##### 9. Question

I.x^{2} + 11x + 30 = 0

II.y^{2} + 12y + 36 = 0

x

^{2}+ 5x + 6x + 30 = 0

X(x + 5) + 6(x + 5) = 0

(x + 5) (x + 6) = 0

x = – 5, – 6

y^{2} + 12y + 36 = 0

y(y + 6) + 6(y + 6) = 0

( y + 6) (y+6) = 0

y = – 6, -6

x ≥ y

##### 10. Question

I.2x^{2} + x – 1 = 0

II.2y^{2} – 3y + l = 0

2x

^{2}+ 2x – x – 1 = 0

2x(x + 1) – 1(x + 1) = 0

(2x – 1) (x + 1) = 0

X= 1/2 ,-1

2y^{2} – 2y – y + 1 = 0

2y(y – 1) – 1(y – 1) = 0

(2y – 1)(y – 1) = 0

Y= 1/2,1

ie x ≤ y