Hello Britt!
To see which system of linear equations obtain the solution (7,0), you just plug in 7 for every x you see and 0 for y. If the equation turns out true then it is a solution. If whatever we get doesn't, it is not an equation.
A) x - y = 7 -> 7 - 0 = 7
Does 7 minus 0 equal 7? Yes, therefore this equation in answer choice A is correct.
x + y = 9 -> 7 + 0 = 9
Does 7 added by 0 equal 9? No, therefore this equation in answer choice A is incorrect.
A cannot be the right answer given that only one equation checks out.
B) 7x + 3y = 10 -> 7(7) + 3(0) = 10 -> 49 + 0 = 10 -> 49 = 10
Is 49 equivalent to 10? No, therefore B is incorrect right off the bat. We can skip the other equation; it wouldn't matter since both equations in the system must have (7,0) as a solution.
C) Just by looking at this, I can deduce that this is the correct answer. 7 - 0 and 7 + 0's sum is 7. 7 is equivalent to (=) 7. However, if you want closure,
D) 3(7) - 4(0) = 21 -> 21 - 0 = 21
Is 21 minus 0, 21? Yes, consequently, this equation in answer choice D is correct.
The second one is obviously incorrect.
3(x) + 4(y) = -20 -> 3(7) + 0 = -20
21 is definitely not equivalent to -20.
In short, C is your answer ;P