To determine which of the given points is a solution to the system of equations:

$5x - y = 9$ $2x + y = 5$

we can substitute each point $(x, y)$ into both equations to check if both equations are satisfied.

1. For $(3, -1)$:

   • First equation: $5(3) - (-1) = 15 + 1 = 16$ (does not equal 9)
   • This point is not a solution.

2. For $(-1, 7)$:

   • First equation: $5(-1) - 7 = -5 - 7 = -12$ (does not equal 9)
   • This point is not a solution.

3. For $(2, 1)$:

   • First equation: $5(2) - 1 = 10 - 1 = 9$ (satisfied)
   • Second equation: $2(2) + 1 = 4 + 1 = 5$ (satisfied)
   • This point is a solution.

4. For $(1, -4)$:

   • First equation: $5(1) - (-4) = 5 + 4 = 9$ (satisfied)
   • Second equation: $2(1) + (-4) = 2 - 4 = -2$ (does not equal 5)
   • This point is not a solution.

Thus, the solution to the system is $(2, 1)$.

Would you like further explanation or have any questions?

Related Questions

1. How can substitution or elimination methods help solve systems of equations?
2. What are the differences between consistent, inconsistent, and dependent systems?
3. How can graphing help visualize the solution to a system of equations?
4. What is the significance of unique, infinite, or no solutions in systems of equations?
5. How can systems of equations be applied to real-world problems?

Tip: Checking each option systematically can quickly eliminate incorrect answers, saving time in multiple-choice math problems.