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Directions: 1-5) **In the following questions, two equations numbered are given in variables x and y. Solve both the equations and find out the relationship between x and y. Then give answer accordingly-**

1.

I. 12p^{2} – 5p – 3 = 0,

II. 3q^{2} – 11q + 6 = 0

2.

I. 6p^{2} + 7p + 2 = 0,

II. 15q^{2} – 38q – 40 = 0

3.

I. 3p^{2} – 25p + 52 = 0

II. 2q^{2} – 7q + 3 = 0

4.

I. p^{2} = 1156

II. q = √1156

5.

I. p^{2} – √3969 = √6561,

II. q^{2} – √1296 = √4096

Directions:6-10) **In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give an answer**

6.

I. (x+3) (y+2)=12

II. 2xy+4x+5y=11

7.

I. (3x-2)/y = (3x+6)/(y+16)

II. (x+2)/(y+4) = (x+5)/(Y+10)

8.

I. x^{2}+20x+4=50-25x

II. y^{2}-10y-24=0

9.

I. (x^{2}-10x+16)/(x^{2} -12x +24) = 2/3

II. y^{2}-y-20=0

10.

a)785+x=846-7^{2 }b)y^2=(1862-1726+2^{3})

**Check your Answers below:**

Directions: 1-5)

**In the following questions, two equations numbered are given in variables x and y. Solve both the equations and find out the relationship between x and y. Then give answer accordingly-**##### 1. Question

I. 12p

^{2}– 5p – 3 = 0,

II. 3q^{2}– 11q + 6 = 0Ans:5

12p^{2}– 5p – 3 = 0

12p^{2}+ 4p – 9p – 3 = 0

Gives p = -1/3, 3/4

3q^{2}– 11q + 6 = 0

3q^{2}– 9q – 2q + 6 = 0

Gives q = 2/3, 3

Put all values on number line and analyze the relationship

-1/3… 2/3… 3/4… 3##### 2. Question

I. 6p

^{2}+ 7p + 2 = 0,

II. 15q^{2}– 38q – 40 = 0Ans:5

6p^{2}+ 7p + 2 = 0

6p^{2}+ 4p + 3p + 2 = 0

Gives p = -2/3, -1/2

15q^{2}– 38q – 40 = 0

15q^{2}+ 12q – 50q – 40 = 0

Gives q = -4/5, 10/3

Put all values on number line and analyze the relationship

-4/5… -2/3… -1/2… 10/3##### 3. Question

I. 3p

^{2}– 25p + 52 = 0

II. 2q^{2}– 7q + 3 = 0Ans:1

3p^{2}– 25p + 52 = 0

3p^{2}– 12p – 13p + 52 = 0

Gives p = 4, 13/3

2q^{2}– 7q + 3 = 0

2q^{2}– 6q – q + 3 = 0

So q = 1/2, 3

Put all values on number line and analyze the relationship

1/2… 3… 4… 13/3p > q

##### 4. Question

I. p

^{2}= 1156

II. q = √1156Ans:4

p^{2}= 1156

So p = -34, 34

q = √1156

So q = 34

Put all values on number line and analyze the relationship

-34… 34p ≤ q

##### 5. Question

I. p

^{2}– √3969 = √6561,

II. q^{2}– √1296 = √4096Ans:5

p^{2}– √3969 = √6561

p^{2}– 63 = 81

p^{2}= 144

So p = -12, 12

q^{2}– √1296 = √4096

q^{2}– 36 = 64

q^{2}= 100

So q = -10, 10

Put all values on number line and analyze the relationship

-12… -10….10…. 12##### 6. Question

Directions:6-10)

**In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give an answer**I. (x+3) (y+2)=12

II. 2xy+4x+5y=11

Ans:5

xy+3y+2x +6 =122xy+6y+4x=12—-(i)

2xy+5y+4x=11 —- (ii)

From eq. (i) — (ii)

Y = 1

From eq. (i)

x=1

x = y

##### 7. Question

I. (3x-2)/y = (3x+6)/(y+16)

II. (x+2)/(y+4) = (x+5)/(Y+10)

Ans: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

x<y

##### 8. Question

I. x

^{2}+20x+4=50-25xII. y

^{2}-10y-24=0Ans:5

x^{2}+20x+4=50-25xx

^{2}+45x-46=0x

^{2}-x+46x-46=0x(x-1)+ 46 (x-1) =0

(x-1)(x+46)=0

X= -46 and 1

y

^{2}-10y-24=0y

^{2}+2y -12y -24=0y(y+2) – 12 (y+2) =0

(y-12) (y+2) =0

Y = 12 and -2

Relationship cannot be established

##### 9. Question

I. (x

^{2}-10x+16)/(x^{2}-12x +24) = 2/3II. y

^{2}-y-20=0Ans:5

(x^{2}-10x+16)/(x^{2}-12x +24) = 2/33x

^{2}-30x+48=2x^{2}-24x+48X

^{2}-6x=0(x) (x-6) =0

X= 6, 0

y

^{2}-y-20=0y

^{2}-5y+4y-20=0y(y-5)+4(y-5)=0

(y+4)(y-5) =0

Y = -4, 5

Relationship cannot be established

##### 10. Question

a)785+x=846-7

^{2}b)y^2=(1862-1726+2

^{3})Ans:4

a)785+x=846-7^{2}785+x=846-49

x=797-785

x=12

b)y^2=(1862-1726+2

^{3})y^2=144

y=12 and -12

**Hence x≥y**