Question

Write a system of equations with the solution (5, 2).

Answer 1

This is one of those questions where they are just trying to confuse you by giving so many possibilities.

(-5, 2) Since (x, y)
x = -5
y = 2

a(x) + b(y) = s a(-5) + b(2) = s
c(x) + d(y) = t c(-5) + d(2) = t

Let's say a = 1, b = -2, c = 4, d = 5. These choices are random since it will work for any numbers.
You just need to solve the totals s and t
x - 2y = s -5 - 2(2) = -9 -5 - 4 = -9 s = -9
4x + 5y = t 4(-5) + 5(2) = -10 -20 + 10 = -10 t = -10

One of any number of solutions
x - 2y = -9
4x + 5y = -10

Solving the system we can show we will end up with our original solution
13y = 26 y = 2 x - 4 = -9 x = -5
(-5, 2)