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 for the systems of equations: System 1: 2x + y = 7 &(1) \\ x + y = 5 &(2) Step 1: Subtract equation (2) from equation (1) to eliminate y. (2x + y) - (x + y) = 7 - 5 \\ 2x + y - x - y = 2 \\ x = 2 Step 2: Substitute x = 2 into equation (2). x + y = 5 \\ 2 + y = 5 \\ y = 5 - 2 \\ y = 3 The solution for the first system is x=2, y=3. --- System 2: 2x + y = 7 &(3) \\ x + y = 2 &(4) Step 1: Subtract equation (4) from equation (3) to eliminate y. (2x + y) - (x + y) = 7 - 2 \\ 2x + y - x - y = 5 \\ x = 5 Step 2: Substitute x = 5 into equation (4). x + y = 2 \\ 5 + y = 2 \\ y = 2 - 5 \\ y = -3 The solution for the second system is x=5, y=-3.