Linear Equation | MCQs

Explanation

Let's solve for x:

6 + 5x = 30 - x

Add x to both sides:

6 + 6x = 30

Subtract 6 from both sides:

6x = 24

Divide both sides by 6:

x = 24/6

x = 4

So, the correct answer is 4.

Explanation

3x - 15 - 6 = 0

3x = 21

X = 21/3

X = 7

Explanation

3x-54 = 36

3x = 90

x = 30

Explanation

The equation |-x| = 0 simplifies to x = 0 since the absolute value of any number is zero only when the number itself is zero.

Therefore, the solution set contains only {0}.

Explanation

Let the cost of 1 chair be Rs. x and the cost of 1 table be Rs. y.

From the first set of values, we get: 3x + 2y = 700 ... (i)

From the second set of values, we get: 5x + 3y = 1100 ... (ii)

Multiply equation (i) by 5: 15x + 10y = 3500 ... (iii)

Multiply equation (ii) by 3: 15x + 9y = 3300 ... (iv)

Subtract equation (iv) from equation (iii): y = 200

Substitute y = 200 in equation (i): 3x + 2(200) = 700 => 3x = 300 => x = 100

Finally, find the cost of 2 chairs and 2 tables: 2x + 2y = 2(100 + 200) = Rs. 600

Explanation

Step 1: Add the two equations to eliminate y

(x + y) + (x - y) = 10 + 10

2x = 202x = 10

Step 2: Solve for x

x = 20/2x = 10

Explanation

To find the value of X, substitute Y = 5 into the equation Y = 3X + 12:

5 = 3X + 12

Subtract 12 from both sides:

-7 = 3X

Divide both sides by 3:

-7/3 = X

So, the value of X is -7/3!

Explanation

We are given the equation:

w = (2/3)t + 6

and asked to find w when t = 12.

Step-by-step:

w = (2/3 × 12) + 6

w = 8 + 6

w = 14

Explanation

Let's solve the equations:

1. x + y = 5

2. x - y = 3

Add both equations:

2x = 8

x = 4

Now, substitute x = 4 in equation (1):

4 + y = 5

y = 1

The solution is (4, 1).

Explanation

a + b = 2 ... (1)

a - b = 2 ... (2)

Adding (1) and (2):

2a = 4

a = 2

Put a = 2 in (1):

2 + b = 2

b = 0

Now, a² + b² = (2)² + (0)² = 4 + 0 = 4.