This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey feisalisrael2, good to see you again. Here are the given equations: ax + by = c (1) ax + by = 0 (2) Step 1: Compare the equations. Both equations have the same coefficients for x (a) and y (b). This means they represent lines with the same slope. Step 2: Analyze the constant terms. The constant term in equation (1) is c, and in equation (2) it is 0. The relationship between the two lines (and thus the number of solutions) depends on the value of c. Step 3: Determine the number of solutions. • Case 1: If c ≠ 0 If c is any non-zero number, then ax + by cannot simultaneously equal c and 0. This means the two equations represent two distinct parallel lines. Parallel lines never intersect, so there is no solution to the system. • Case 2: If c = 0 If c is equal to 0, then both equations become ax + by = 0. This means the two equations are identical. They represent the same line. In this case, there are infinitely many solutions, as any point (x, y) that satisfies ax + by = 0 is a solution to the system. The number of solutions depends on the value of c: If c ≠ 0, there is no solution. If c = 0, there are infinitely many solutions. Send me the next one 📸