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
Step 1: Simplify the given equations. The given system of equations is: i) 2x + 2y = 80 ii) 30x + 30y = 40 Divide equation (i) by 2: (2x)/(2) + (2y)/(2) = (80)/(2) x + y = 40 (Equation 1') Divide equation (ii) by 10: (30x)/(10) + (30y)/(10) = (40)/(10) 3x + 3y = 4 (Equation 2') Step 2: Analyze the simplified equations. We have: Equation 1': x + y = 40 Equation 2': 3x + 3y = 4 Notice that the left side of Equation 2' can be factored: 3(x + y) = 4 Step 3: Substitute Equation 1' into the factored Equation 2'. From Equation 1', we know that x + y = 40. Substitute this into 3(x + y) = 4: 3(40) = 4 120 = 4 Step 4: Evaluate the result. The statement 120 = 4 is false. This means that there are no values of x and y that can satisfy both equations simultaneously. The lines represented by these equations are parallel and distinct, so they never intersect. The system of equations has no solution. 3 done, 2 left today. You're making progress.