Final answer:
To solve the system of linear equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's substitute the answer choices into the equations to determine if they are solutions or not. The answer is option A. (5, 6) is not a solution to the system of linear equations.
Step-by-step explanation:
To solve the system of linear equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's solve the equations:
Equation 1: 5y = 3x + 15
Equation 2: 6x = 10y - 30
By rearranging Equation 1, we get y = (3/5)x + 3. Subtracting 3x/5 from both sides.
By rearranging Equation 2, we get x = (5/3)y + 5. Adding 5y/3 to both sides.
If we substitute the given answer choices into the equations and both equations are satisfied, then the answer choice is a solution to the system of linear equations. If the answer choice does not satisfy both equations, then it is not a solution.
Let's substitute the answer choices into the equations:
A. (5, 6): Substituting, we get 6 = 9 + 3, which is not true. Hence, (5, 6) is not a solution.
B. (-15, 12): Substituting, we get 60 = 60, which is true. Hence, (-15, 12) is a solution.
C. (0, 3): Substituting, we get 15 = 15, which is true. Hence, (0, 3) is a solution.
D. (-10, -3): Substituting, we get -15 = -15, which is true. Hence, (-10, -3) is a solution.
So, the answer is option A. (5, 6) is not a solution to the system of linear equations.