It is known that the two solutions of binary linear equation AX + by + 2 = 0 are respectively x = 1, y = 4, x = - 3, y = - 4. Please solve the following problems: (1) solve the equation; (2) represent all the solutions of the equation with images | Math enthusiast | Mathematical art

It is known that the two solutions of binary linear equation AX + by + 2 = 0 are respectively x = 1, y = 4, x = - 3, y = - 4. Please solve the following problems: (1) solve the equation; (2) represent all the solutions of the equation with images

1: Take x = 1, y = 4 into ax + by + 2 = 0 to get a + 4B + 2 = 0, take x = - 3, y = - 4 into ax + by + 2 = 0 to get - 3a-4b + 2 = 0, solve these two equations to get a = 2, B = - 1, then take a = 2, B = - 1 into ax + by + 2 = 0 to get equation 2x-y + 2 = 0, that is, y = 2x + 22: the intersection points of this equation on X axis and Y axis are (0,2) (1,4) respectively

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