1. The first step to solving this problem is to find the values of x and y. This can be done in a multitude of different ways, however I will go with the method of substitution.
Thus, the first thing we must do is write out both equations and rearrange one of them so that either x or y is the subject of the equation. Looking at the two equations, I can see that in the second equation this would be easier, and that we could also simplify the first equation a little further. Thus:
a) Collecting like terms to simplify equation 1:
4x + 3y = 14 - y
4x + 4y = 14 (Add y to both sides)
b) Rearranging equation 2 to make x the subject:
x - 5y = 2
x = 2 + 5y (Add 5y to both sides)
Now, we can substitute x = 2 + 5y into the first equation:
4x + 4y = 14
if x = 2 + 5y:
4(2 + 5y) + 4y = 14
8 + 20y + 4y = 14 (Expand 4(2 + 5y))
8 + 24y = 14 (Add 20y and 4y)
24y = 6 (Subtract 8 from both sides)
y = 1/4 (Divide both sides by 24)
Now that we know that y = 1/4, we can substitute this back into x = 2 + 5y:
x = 2 + 5y
if y = 1/4: x = 2 + 5(1/4)
x = 2 + 5/4
x = 13/4
2. So now we know that x = 13/4 and y = 1/4. Given these values, we can now solve x - y as such:
x - y = 13/4 - 1/4
= 12/4
= 3
Thus, the value of x - y is 3 (answer C).
