Linear Equation problems
- 1. If 2x + 3y = 29 and y = x + 3, what is the value of x?
Options- A. 4
- B. 5
- C. 6
- D. 7 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 4
Explanation:
2x + 3y = 29 ...(i)
and y = x + 3 ...(ii)
Putting the value of y from Eq. (ii) to Eq. (i), we get
2x + 3y = 29
2x + 3(x + 3) = 29
2x + 3x + 9 = 29
? 5x = 20
? x = 4
- 2. If 3x + 7y = 75 and 5x - 5y = 25, what is the value of x + y?
Options- A. 14
- B. 15
- C. 16
- D. 17 Also asked in: Bank Exams
Correct Answer: 17
Explanation:
3x + 7y = 75 ..(i)
5x - 5y = 25
? x - y = 5 ...(ii)
On multiplying Eq. (ii) by 7 and adding to Eq. (i), we get
3x + 7y = 75
7x - 7y = 35
------------------
10x = 110
x = 11
? Putting the value of x in Eq. (ii), we get
11 - y = 5
? y = 6
? x + y = 6 + 11 = 17
- 3. If x + y - 7 = 0 and 3x + y - 13 = 0, then what is 4x 2 + y 2 + 4xy equal to?
Options- A. 75
- B. 85
- C. 91
- D. 100 Discuss
Correct Answer: 100
Explanation:
we have, x + y - 7 = 0
? x + y = 7 ...(i)
and 3x + y - 13 = 0
? 3x + y = 13 ..(ii)
By subtracting Eq. (i) from Eq. (ii), we get
3x + y = 13
x + y = 7
----------------------
2x = 6 ...(ii)
? x = 3
On putting the value of x in Eq. (i), we get
3 + y = 7
? y = 4
Now, 4x2 + y2 + 4xy
= 4 x (3)2 + (4)2 + 4 x 3 x 4
= 4 x 9 + 16 + 48
= 36 + 16 + 48 = 100
- 4. if 3 x + y = 81 and 81 x - y = 3, then what is the value of x?
Options- A. 17/16
- B. 17/8
- C. 17/4
- D. 15/4 Discuss
Correct Answer: 17/8
Explanation:
Given, 3x + y = 81
? 3x + y = 34
? x + y = 4 ...(i)
and 81x - y = 3 or (34)x - y = 3
? x - y = 1/4
On solving the Eqs. (i) and (ii), we get
2x = 17/4 ? x = 17/8
- 5. solve 6x + 3y = 7xy and 3x + 9y = 11xy.
Options- A. x=1, y=3/2
- B. x=-1, y = 3/2
- C. x=3/2, y=1/2
- D. x=1, y= -3/2 Discuss
Correct Answer: x=1, y=3/2
Explanation:
Given equation are 6x + 3y = 7xy
? (6/y) + (3/x) = 7 .....(i)
And 3x + 9y = 11xy
? (3/y) + (9/x) = 11 .....(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i), we get
(6/y) + (3/x) = 7
(6/y) + (18/x) = 22
-------------------------
- 15/x = - 15
? x = 1
On putting this value in Eq. (i), we get
(6/y) + 3 = 7
? 6/y = 4
? y = 6/4 = 3/2
- 6. Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has?
Options- A. 32
- B. 36
- C. 34
- D. Cannot be determined Discuss
Correct Answer: 34
Explanation:
Let hens = H, goats = G
According to the question,
H + G = 90 ...(i)
2H + 4G = 248 ...(ii)
On multiplying Eq. (i) by 2 and subtracting from Eq. (ii) , we get
2H + 2G = 180
2H + 4G = 248
-------------------
-2G = -68
? G = 34
- 7. The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits?
Options- A. 56
- B. 63
- C. 42
- D. Cannot be determined Discuss
Correct Answer:
Explanation:
Let the number be x and y.
Then, according to the question,
x + y = 15 ...(1)
x - y = 3 ...(ii)
on adding Eqs. (i) and (ii), we get
2x = 18
? x = 9
On putting the value of in Eq. (i), we get
y = 6
? Product = xy = 54
- 8. The numerator of a fraction is 6x + 1 and the denominator is 7 - 4x, x can have any value between -2 and 2, both included. The values of x for which the numerator is greater
Options- A. 3/5 < x ? 2
- B. 3/5 ? x ? 2
- C. 0 < x ? 2
- D. -2 ? x < 2 Discuss
Correct Answer: 3/5 < x ? 2
Explanation:
6x + 1 > 7 - 4x
? x > 3/5
? 3/5 < x ? 2
- 9. If (x/4) + (y/3) = 10/24 and (x/2) + y = 1, then the value of x + y is
Options- A. 1
- B. 3/2
- C. 2
- D. 4 Discuss
Correct Answer: 3/2
Explanation:
Given, (x/4) + (y/3) = 10/24
? (3x + 4y)/12 = 10/24
? 3x + 4y = 5 ...(i)
and (x/2) + y = 1
x + 2y = 2 ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i).
3x + 4y = 5
2x + 4y = 4
- - -
--------------------------
x = 1
On putting the value of x in Eq. (ii), we get
x + 2y = 2
? 1 + 2y = 2
? y = 1/2
? x + y = 1 + 1/2 = 3/2
- 10. The cost of 21 pencil and 9 clippers is ? 819. What is the total cost of 7 pencils and 3 clippers together?
Options- A. ? 204
- B. ? 409
- C. ? 273
- D. ? 208 Discuss
Correct Answer: ? 273
Explanation:
Let cost of 1 pencil and 1 clipper be p and c, respectively.
Now, according to the question,
21p + 9c = ? 819
? 3(7p + 3c) = ? 819
? 7p + 3c = ? 273
Cost of 7 pencil and 3 clippers = ? 273
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