Final answer:
To determine the number of solutions for a system of linear equations, known values should be listed, and equations should be solved systematically. After solving, the answer should be reviewed for reasonableness in terms of units and magnitude.
Step-by-step explanation:
The student's question relates to finding the number of solutions of a system of linear equations where 'a' is a real number. To solve this, one must first list all the known values and then identify what they need to solve for. This may require creating a table to organize the information. Once the variables and constants are clear, you can proceed to solve the simultaneous equations for the unknowns. Solving these equations can be a multi-step algebraic process requiring careful attention to detail. After obtaining the solution, it is important to examine the answer to ensure that it is reasonable, checking that units are correct and the magnitude of the numbers makes sense.
This approach is essential in determining the number of solutions. This process is typically used for problems such as when the constants are given as a = 1.00, b = 10.0, and c = -200 and the solutions for the linear equations or quadratic equations are required. It is also important to note that, depending on the values of the constants and coefficients in the equations, the system may have one solution, no solution or infinitely many solutions, which is determined after solving the equations.