Algebraic Expressions

x = (6X8)/4 = 12 Now, 2y + 12 = 7 Or y = - 5/2

z = 1, k + s = 2, 3(y + 1) = 2y X 2, 3y + 3 = 4y, y = 3

12 + 0 - (-4) = 16

3{(x.y + y.z + x.z)} + 1 = 3{(1) (2) + (2) (0) + (1) (0)} + 1 = 3 X 2 + 1 = 6 + 1 = 7

Using the definition x ^ y = 2x + y, evaluate both sides: 2 ^ a = 2(2) + a = 4 + a, and a ^ 3 = 2(a) + 3 = 2a + 3. Setting them equal: 4 + a = 2a + 3. Solving: 4 - 3 = 2a - a, so 1 = a. Verifying: 2 ^ 1 = 5 and 1 ^ 3 = 5, both equal.

From 9x - 3y = 12, divide by 3: 3x - y = 4. From 3x - 5y = 7. Solving these simultaneously: Subtract second from first: 4y = -3, so y = -3/4. Then 3x = 4 + y = 13/4, x = 13/12. Therefore 6x - 2y = 2(3x - y) = 2(4) = 8.

Given x = y = 2z and xyz = 256. Let z = k, then x = y = 2k. So xyz = (2k)(2k)(k) = 4k^3 = 256, giving k^3 = 64, so k = 4. Therefore x = 2k = 8.

Multiply the given equation 2x-y=4 by 3 on both sides. This gives 6x-3y=12. When you multiply an entire equation by a constant, the equality still holds.

Yes, it is the correct answer. Option 2 is the answer.

First calculate --y = -11 (pre-decrement), then x++ uses 5 (post-increment, x becomes 6 after). The expression --y * b / a = -11 * 2 / 4 = -22 / 4 = -5 (integer division). So z = 5 - (-5) = 10. Remember operator precedence: postfix ++ has highest precedence, then prefix --, then *, /, then +, -.

(x + 2y - 2z)/(x - 2y + 2z) = (2 + 2 - 2)/(2 - 2 + 2) = 1 Hence, this option is incorrect.

(x + y)² = x² + y² + 2xy = 10 + 2.2 = 14 Hence, this option is correct.

Convert both to base 10: 7x + 3 = 5y + 4. This simplifies to 7x - 5y = 1. Testing the options: for x=8, 56+3=59; 5y+4=59 implies 5y=55, so y=11.

y - 2 = 2k + (a - 3) => y - 2 = 2 X 2 + (5 - 3) => y - 2 = 4 + 2 => y = 6 + 2 = 8

Adding the two equations, 200x + 200y = 1000 Or 200(x + y) = 1000 Or x + y = 5