Answer:To find the value of 5x + 6y, we need to solve the system of equations:
2x - 4y = 4 (Equation 1)
4x + 6y = 8 (Equation 2)
We can use the method of elimination to solve this system.
First, let's multiply Equation 1 by 2 to make the coefficients of x in both equations the same:
4x - 8y = 8 (Equation 3)
Next, let's add Equation 2 and Equation 3 together:
(4x + 6y) + (4x - 8y) = 8 + 8
8x - 2y = 16 (Equation 4)
Now, let's solve Equation 4 for x:
8x = 16 + 2y
x = (16 + 2y) / 8
x = 2 + (1/4)y
We can substitute this value of x back into Equation 2:
4(2 + (1/4)y) + 6y = 8
8 + 2y + 6y = 8
8y = 0
y = 0
Now, substitute the value of y back into the expression 5x + 6y:
5x + 6(0) = 5x
5x = 5x
The value of 5x + 6y is 5x, which means it depends on the value of x. Since we have expressed x in terms of y as x = 2 + (1/4)y, the value of 5x + 6y can vary depending on the value of y.
Therefore, the value of 5x + 6y is not a specific number but is dependent on the values of x and y in the given system of equations.
Step-by-step explanation: