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Directions:1-10)** In the following questions, two equations I and II are given. You have to solve both the equations and g****ive Answer as,**

1.

I) 4x-3y-2=0

II) 6x+y-36=0

2.

I) x^{2}-4x-621=0

II) y^{2}-35y+276=0

3.

I) 3x^{2}+25x-18=0

II) 18y^{2}-41y+21=0

4.

I) 6x^{2}+x-2=0

II) 30y^{2}+11y+1=0

5.

I) x^{3}=1728

II) y^{2}=144

6.

- 5x
^{2}– 18x + 9 = 0 - 20y
^{2}– 13y + 2 = 0

7.

- x
^{3}– 878 = 453 - y
^{2}– 82 = 39

8.

- 3/√x + 4/√x = √x
- y
^{3}– (7)^{7/2}/√y = 0

9.

- 9x – 15.45 = 54.55 + 4x
- √(y + 155) – √36 = √49

10.

- x
^{2}+ 11x + 30 = 0 - y
^{2}+ 7y + 12 = 0

**Check your Answers below:**

Directions:1-10)

**In the following questions, two equations I and II are given. You have to solve both the equations and g****ive Answer as,**##### 1. Question

**I) 4x-3y-2=0****II) 6x+y-36=0**Ans:2

I) 4x-3y-2=0 …………..(1)II) 6x+y-36=0 …………………. (2)After solving (i) and (ii), we have

x=5 and y=6

**Hence x<y**##### 2. Question

**I) x**^{2}-4x-621=0**II) y**^{2}-35y+276=0Ans:5

I) x^{2}-4x-621=0x^{2}-27x+23x-621=0(x-27)(x+23)=0

x=27 or -23

II) y

^{2}-35y+276=0y

^{2}-23y-12y+276=0(y-23)(y-12)=0

y=23 or 12

**Hence the relationship cannot be determined.**##### 3. Question

I) 3x

^{2}+25x-18=0II) 18y

^{2}-41y+21=0Ans:2

I) 3x^{2}+25x-18=03x^{2}+27x-2x-18=0(x+9) (3x-2) =0

x=2/3 or -9

II) 18y

^{2}-41y+21=018y

^{2}-27y-14y+21=0(2y-3)(9y-7)=0

y=3/2 or 7/9

**Hence x<y**##### 4. Question

I) 6x

^{2}+x-2=0II) 30y

^{2}+11y+1=0Ans:5

I) 6x^{2}+x-2=06x^{2}-3x +4x -2 =0(2x-1)(3x+2)=0

x=1/2 or -2/3

II) 30y

^{2}+11y+1=030y

^{2}+6y+5y+1=0(5y+1)(6y+1)=0

y=-1/5 or -1/6

**Hence the relationship cannot be determined.**##### 5. Question

I) x

^{3}=1728II) y

^{2}=144Ans:3

I) x^{3}=1728x=12II) y

^{2}=144y=12 or -12

**Hence x ≥ y**##### 6. Question

**5x**^{2}– 18x + 9 = 0**20y**^{2}– 13y + 2 = 0

Ans:1

I. 5x^{2}– 18x + 9 = 05x^{2}– 15x – 3x + 9 = 05x (x -3) – 3(x – 3) = 0

(x – 3) (5x – 3) = 0

x = 3 or 3/5

II. 20y

^{2}– 13y + 2 = 020y

^{2}– 8y – 5y + 2 = 04y(5y – 2) -1(5y – 2) = 0

(4y – 1) (5y – 2) = 0

y = 1/4 or 2/5

**Clearly x > y**##### 7. Question

- x
^{3}– 878 = 453 - y
^{2}– 82 = 39

Ans:2

I. x^{3}– 878 = 453x =^{3}√1331 = 11x = 11

II. y

^{2}– 82 = 39y

^{2}= 82 + 39 = 121y = ±11

**Hence x ≥ y**- x
##### 8. Question

**3/√x + 4/√x = √x****y**^{3}– (7)^{7/2}/√y = 0

Ans:5

I. 3/√x + 4/√x = √x3 +4 = xx = 7

II. y

^{3}– (7)^{7/2}/√y = 0y

^{3+1/2}– (7)^{7/2}= 0y

^{7/2}= 7^{7/2}y = 7

**Clearly, x = y**##### 9. Question

- 9x – 15.45 = 54.55 + 4x
- √(y + 155) – √36 = √49

Ans:5

I. 9x – 15.45 = 54.55 + 4x

9x – 4x = 705x = 70x = 14

II. √(y + 155) – √36 = √49

√(y + 155) = 6 + 7

√(y + 155) = 13

y + 155 = 169

y = 169 – 155 = 14

**Clearly, x = y**##### 10. Question

- x
^{2}+ 11x + 30 = 0 - y
^{2}+ 7y + 12 = 0

Ans:3

I. x^{2}+ 11x + 30 = 0x^{2}+ 6x + 5x + 30 = 0x(x +6) + 5(x + 6) = 0

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

x = -5 (or) -6II. y

^{2}+ 7y + 12 = 0y

^{2}+ 4y + 3y + 12 = 0y(y+4) + 3(y+4) = 0

(y+3) (y+4) = 0

y = -3 (or) -4

**Hence x<y**- x