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Answer 1

Для решения данной системы уравнений графическим способом, нужно построить графики обоих уравнений на координатной плоскости и найти точку их пересечения. 1. Уравнение x + y = 2 представляет собой прямую линию. Чтобы построить ее график, нужно найти две точки, которые принадлежат этой прямой. Для этого можно присвоить x значение 0 и найти соответствующее значение y, а затем присвоить y значение 0 и найти соответствующее значение x. При x = 0, получаем: 0 + y = 2, откуда y = 2. Таким образом, у нас есть точка (0, 2). При y = 0, получаем: x + 0 = 2, откуда x = 2. Таким образом, у нас есть точка (2, 0). Построим прямую, проходящую через эти две точки. 2. Уравнение y = -x^2 - 2x + 4 представляет собой параболу. Чтобы построить ее график, можно использовать точки, которые удовлетворяют уравнению. Для этого можно присвоить значения x и найти соответствующие значения y. При x = -2, получаем: y = -(-2)^2 - 2(-2) + 4 = -4 + 4 + 4 = 4. Таким образом, у нас есть точка (-2, 4). При x = 0, получаем: y = -(0)^2 - 2(0) + 4 = 0 - 0 + 4 = 4. Таким образом, у нас есть точка (0, 4). При x = 2, получаем: y = -(2)^2 - 2(2) + 4 = -4 - 4 + 4 = -4. Таким образом, у нас есть точка (2, -4). Построим параболу, проходящую через эти три точки. Теперь найдем точку пересечения графиков прямой и параболы. Эта точка будет являться решением системы уравнений. По графику можно определить, что точка пересечения находится примерно в точке (1, 1). Таким образом, решение системы уравнений x + y = 2 и y = -x^2 - 2x + 4 равно x = 1 и y = 1.