# Basic Equations - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Basic Equations. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz. Q 1 - On solving 2x+y=8 and 3y=4+4x, we get:

A - x=3, y=-4

B - x=2, y=4

C - x=1, y=4

D - x=4, y=1

### Explanation

```The given equations are
2x+ y=8...  (1)     4x-3y=-4 ...(2)
On multiplying (1) by 3 and adding (2) to it, we get:
10x= 20
⇒x= 2
Putting x= 2 in (1), we get: 4+ y = 8   ⇒y = 4
∴ x= 2, y= 4```

Q 2 - On solving 4/x+5y=7 and 3/x+4y =5 we, get:

A - x=1/3, y=1

B - x=- 1/3, y=-1

C - x=1/3, y=-1

D - x=- 1/3, y=1

### Explanation

```Given equations are 4/x+5 y= 7 ...(i)
3/x+4y = 5  ...(ii)
On multiplying (i) by 3, (ii) by 4 and subtracting, we get -y =1 ⇒y= -1
Putting y= -1 in (i), we get 4/x-5 = 7 ⇒4/x= 12 ⇒12x= 4 ⇒x= 1/3
∴x= 1/3, y= -1```

Q 3 - If 3x+7y= 75 and 5x-5y= 25, then what is the estimation of x+y?

A - 14

B - 15

C - 16

D - 17

### Explanation

```Given 3x+7y = 75  ...(i)
5x-5 y= 25 ⇒x-y = 5...(ii)
Multiplying (ii) by 7 and adding to (i), we get:
10 x = 110   ⇒x = 11
Putting x = 11 in (ii), we get: y=(11-5) = 6
∴ x+y = (11+6) = 17```

Q 4 - If x/4 + y/3= 5/12 and x/2+ y =1, then the estimation of (x+y) is:

A - 1/2

B - 1

C - 3/2

D - 2

### Explanation

```Given equations are 3x+4y= 5 ...(i) and x+2y =2 ...(ii)
On multiplying (ii) by 3 and subtracting (i) from it, we get 2y = 1 ⇒y = 1/2
Putting y = 1/2 in (ii), we get x+2*1/2 = 2 ⇒x+1= 2 ⇒x =1
∴(x+y ) = (1+1/2 ) = 3/2```

Q 5 - On the off chance that 2a+3 b= 17 and 2a+2-3b+1= 5 then:

A - a=2, b=3

B - a=-2, b=3

C - a=2, b=-3

D - a=3, b=2

### Explanation

```Given equation are  2a +3b = 17 ...(i)
2a*22- 3b*3ⁱ= 5   ⇒4*2a- 3*3b= 5 ...(ii)
Putting 2a = x and 3b= y, we get:
x+y= 17 ...(iii)     4x-3y = 5...(iv)
Multiplying (iii) by 3 and adding (iv) to it, we get: 7x= 56
⇒x= 8
Putting x= 8 in (iii), we get: 8+ y = 17 ⇒y = 9
∴ (2a= 8 = 23 ⇒a = 3) and (3b= 9= 32 ⇒b= 2)
∴ a= 3, b= 2```

Q 6 - On the off chance that 4x+6y =32 and 4x-2y= 4, then 8y =?

A - 24

B - 30

C - 36

D - none of these

### Explanation

```4x+6y = 32...(i) 4x-2y = 4...(ii)
On subtracting (ii) from (i), we get: 8 y= 28```

Q 7 - The arrangement of x/2+y/3 =4 and x+y = 10 are given by:

A - x=6, y=-4

B - x=-6, y=4

C - x=4, y=6

D - x=6, y=4

### Explanation

```Given equation are 3x+2y = 24 ...(i), x+y =10 ...(ii)
On multiplying (ii) by 2 and subtracting from (i), we get: x=4
Putting x= 4 in (ii), we get: y = (10-4) = 6```

Q 8 - The arrangement of mathematical statements 2x+ℏy= 11 and 5x-7y = 5 have no arrangement when:

A - ℏ= 13/5

B - ℏ=-13/5

C - ℏ=-14/5

D - ℏ=-16/5

### Explanation

```For no solution , we have a₁/a₂ = b₁/b₂ ≠c₁/c₂
i.e. 2/5 = ℏ/-7 ≠11/5 ⇒ℏ= -14/5 ```

### Explanation

```Here a₁/a₂= 1/2, b₁/b₂=2/4=1/2 and c₁/c₂=3/3=1.
∴ a₁/a₂=b₁/b₂≠c₁/c₂.
∴Give system has no solution.```

Q 10 - In the event that 3x-5y = 5 and x/x+y = 5/7, then (x-y) =?

A - 3

B - 4

C - 6

D - 9

### Explanation

```3x -5y=5 ...(i), 7x=5x+5y⇒2x-5y=0 ...(ii)
On subtracting (ii) from (i), we get=5.
3*5-5y=5⇒5y=10⇒y=2.
∴(x-y) = (5-2) =3.```

aptitude_basic_equations.htm 