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
Here are the solutions to the simultaneous equations using both elimination and substitution methods. 1. Equations: 3x - y = 8 (1) 5x + y = 13 (2) Elimination Method: Step 1: Add equation (1) and equation (2) to eliminate y. (3x - y) + (5x + y) = 8 + 13 8x = 21 x = (21)/(8) Step 2: Substitute the value of x into equation (1). 3((21)/(8)) - y = 8 (63)/(8) - y = 8 y = (63)/(8) - (64)/(8) y = -(1)/(8) The solution is x = (21)/(8), y = -(1)/(8). Substitution Method: Step 1: From equation (1), express y in terms of x. y = 3x - 8 (3) Step 2: Substitute equation (3) into equation (2). 5x + (3x - 8) = 13 8x - 8 = 13 8x = 21 x = (21)/(8) Step 3: Substitute the value of x back into equation (3). y = 3((21)/(8)) - 8 y = (63)/(8) - (64)/(8) y = -(1)/(8) The solution is x = (21)/(8), y = -(1)/(8). 2. Equations: 6x + 2y = 11 (1) 2x + 3y = 1 (2) Elimination Method: Step 1: Multiply equation (2) by 3 to make the coefficients of x equal. 3(2x + 3y) = 3(1) 6x + 9y = 3 (3) Step 2: Subtract equation (3) from equation (1). (6x + 2y) - (6x + 9y) = 11 - 3 -7y = 8 y = -\