Question

solve the system.
2x - 5y = -8
2x - 5y = 12
which statement is true?
a. the solution is (1, 2).
b. the system has no solution.
c. the system has infinitely many solutions.

Explanation:

Step1: Analyze the two equations

We have the system of equations:
$$2x - 5y = -8$$
$$2x - 5y = 12$$
Let's denote the left - hand side of both equations as \(L = 2x-5y\).

Step2: Subtract the equations or analyze the equality

If we subtract the first equation from the second equation (or vice - versa), we get:
\((2x - 5y)-(2x - 5y)=12-(-8)\)
Simplifying the left - hand side: \(2x - 5y-2x + 5y=0\)
Simplifying the right - hand side: \(12 + 8=20\)
So we have \(0 = 20\), which is a contradiction.
Another way to think about it is: The left - hand sides of both equations are the same (\(2x - 5y\)), but the right - hand sides are different (\(-8\) and \(12\)). A single expression \(2x - 5y\) cannot be equal to two different values at the same time. So, there are no values of \(x\) and \(y\) that can satisfy both equations simultaneously.

Answer:

B. The system has no solution.