Explanation

1) 3x - 6y = 15  

2) -2x + 4y = -10

Step 1: Multiply equation (2) by 1.5 to align y coefficients with equation (1):

-2x + 4y = -10  

× 1.5 →  

-3x + 6y = -15

Step 2: Add equation (1) and the modified equation (2):

(3x - 6y) + (-3x + 6y) = 15 + (-15)  

0 = 0

This means the two equations are dependent — they represent the same line.

Step 3: Express x in terms of y from equation (1):

3x - 6y = 15  

3x = 15 + 6y  

x = (15 + 6y) / 3 = 5 + 2y

Since infinitely many solutions exist, pick y = 0:

x = 5 + 2(0) = 5  

y = 0

x = 5, y = 0

Explanation

2√(x + 2) = 3√2

Step-by-step solution:

Step 1: Divide both sides by 2

√(x + 2) = (3√2)/2

Step 2: Square both sides

x + 2 = [(3√2)/2]²  

= (9 × 2) / 4  

= 18 / 4  

= 4.5

Step 3: Subtract 2 from both sides

x = 4.5 − 2  

x = 2.5

Explanation

The square root of 169 is 13, since 13 multiplied by 13 (13²) equals 169.

Explanation

3x + 3 = 4

Subtract 3 from both sides:

3x = 1

Divide by 3:

x = 1/3

Explanation

7x - 2 = 3

Add 2 to both sides:

7x = 5

Divide by 7:

x = 5/7

Explanation

7x + 14 = 21

Subtract 14 from both sides:

7x = 7

Divide by 7:

x = 1

Explanation

Let the two-digit number be 10x + y, where x is the tens digit and y is the unit digit.

Given: x + y = 8

If digits are interchanged, the new number is 10y + x.

Given condition: (10x + y) - (10y + x) = 36

Simplifying: 9x - 9y = 36 → x - y = 4

Solving x + y = 8 and x - y = 4, we get x = 6, y = 2.

The number is 62.

Explanation

a^4 x a^8 x a^3 =?

a^4 has an exponent of 4.

a^8 has an exponent of 8.

a^3 has an exponent of 3.

Add the exponents together: 4 + 8 + 3 = 15.

Therefore, a^4 x a^8 x a^3 simplifies to a^15.

Explanation

3x - 15 - 6 = 0

3x = 21

X = 21/3

X = 7

Explanation

2x + 9x = 11

Combine like terms:

11x = 11

Divide both sides by 11:

x = 1

So, the value of 'X' is 1.