The point (5, -3) is a solution to which system? A. y = x - 8 2x + y = 7 B. y = x + 5 y = x - 3 C. y = x - 5 y = x + 3 D. y = x - 8 -2x + y = 7

Answer 1

To determine which system of equations has (5, -3) as a solution, we need to substitute the point into each of the given equations and see if they hold true.

Option A:

1. $y=x-8$ $$-3=5-8$$ $$-3=-3$$ (True)

2. $2x+y=7$ $$2(5)+(-3)=7$$ $$10-3=7$$ $$7=7$$ (True)

Both equations in Option A are satisfied, so (5, -3) is a solution to this system.

Option B:

1. $y=x+5$ $$-3=5+5$$ $$-3=10$$ (False)

This option does not hold.

Option C:

1. $y=x-5$ $$-3=5-5$$ $$-3=0$$ (False)

This option does not hold.

Option D:

1. $y=x-8$ $$-3=5-8$$ $$-3=-3$$ (True)

2. $-2x+y=7$ $$-2(5)+(-3)=7$$ $$-10-3=7$$ $$-13=7$$ (False)

This option does not hold.

Based on the checks, the only option in which (5, -3) is a solution is Option A:

• $y=x-8$ and $2x+y=7$.

So, the correct answer is A.