If x + y = 6 and 4x – y = 4, what is the value of x?

To find the value of x from the given system of linear equations, we can use the elimination method. The equations are:

• x + y = 6 (Equation 1)
• 4x - y = 4 (Equation 2)

Notice that the 'y' terms have opposite signs. By adding Equation 1 and Equation 2, the 'y' terms will cancel out:

(x + y) + (4x - y) = 6 + 4

5x = 10

Dividing by 5 gives x = 2. Options A, C, and D are incorrect values that would not satisfy both equations simultaneously.