No, this is not a function. The graph would have a vertical line at x=-14. Since there are more than one y value for every given x value, the equation does not represent a function. The slope of the equation also does not exist.
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x-14 = 20 x = 20+14 x = 34
Multiply first equation by 2: 4x - 2y = 20 Subtract second equation: x = 12, so y = 14.
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why will the equations x+14=37 and x-14=37 have different solutions for x
It is not possible to solve one equation in two unknowns (x and y). Two independent equations are required.