2x+y=41 x=y-39 y=2x-41 y=-2x+41 x=2y+41

No single solution satisfies all five equations; only subsets are consistent. For 2x + y = 41, y = -2x + 41, and x = 2y + 41, the solution is x = 24.6, y = -8.2. Explanation 1. Identify the system of equations There are 5 equations with variables x and y. 2. Solve two equations for x and y Use 2x + y = 41 and x = y - 39. Substitute x into the first equation: 2(y-39) + y = 41 \implies 2y - 78 + y = 41 \implies 3y = 119 \implies y = 39.67, x = 0.67. 3. Check consistency with other equations Substitute (x, y) into y = 2x - 41: 39.67 = 2(0.67) - 41 = 1.34 - 41 = -39.66 (not equal). Not consistent. 4. Try another pair Use 2x + y = 41 and y = -2x + 41. Substitute y: 2x + (-2x + 41) = 41 \implies 41 = 41. Infinite solutions along y = -2x + 41. 5. Check which pairs are consistent Test x = 2y + 41 and y = -2x + 41. Substitute x: y = -2(2y + 41) + 41 = -4y - 82 + 41 = -4y - 41 \implies 5y = -41 \implies y = -8.2, x = 2(-8.2) + 41 = -16.4 + 41 = 24.6. 6. Verify all equations with this solution Substitute (x, y) = (24.6, -8.2) into all equations: - 2x + y = 2(24.6) + (-8.2) = 49.2 - 8.2 = 41 ✔️ - x = y - 39 = -8.2 - 39 = -47.2 ✗ - y = 2x - 41 = 2(24.6) - 41 = 49.2 - 41 = 8.2 ✗ - y = -2x + 41 = -2(24.6) + 41 = -49.2 + 41 = -8.2 ✔️ - x = 2y + 41 = 2(-8.2) + 41 = -16.4 + 41 = 24.6 ✔️ 7. List all possible solutions Only equations 2x + y = 41, y = -2x + 41, and x = 2y + 41 are consistent with (x, y) = (24.6, -8.2). No single (x, y) satisfies all five equations.