Answer:
A. One Solution
Explanation:
To determine if a system of equations has no solutions, infinitely many solutions, or exactly one solution, we can solve the system by any method, such as elimination or substitution.
In this case, we can solve the system by elimination. Multiplying the first equation by -2 and adding it to the second equation, we get:
0x + 4y = -3
This equation tells us that y must be equal to -3/4, but we still need to check if this value of y satisfies the original equations. Substituting -3/4 for y in the first equation, we get:
2x + (-3/4) = 7
Solving this equation for x, we get x = 5/4. Substituting this value of x and -3/4 for y in the second equation, we get:
-2(5/4) + 2(-3/4) = -5
which simplifies to:
-5/2 + (-3/2) = -5
This equation is true, so the solution of the system is x = 5/4 and y = -3/4. Since the system has a unique solution, the answer is (A) One Solution.