How do I solve simultaneous equations when one is quadratic? For example 3x^2 -2y = 19, 6x-y-14=0
The aim of this question is to find the two solutions which satisfy the quadratic equation. The approach to this can be broken down into a few principle steps: 1) Express y in terms of x. Here 6x-y-14=0 can be simply rearranged to y = 6x-14 2) Substitute this new definition of y into the other equation so that we have a quadratic equation, all in terms of x3x^2 -2y = 19 becomes 3x^2 -2(6x-14) = 19, which can be rearranged to the quadratic x^2-4x+3 = 03) Solve the quadratic for x: Rearrange the formula to (x-1)(x-3) = 0, which gives the two solutions for x as 3 or 1 4) To complete the solution by solving the value of y for each of the two x values:Considering y=6x-14, When x=1, y = 6x1-14 = -8; By the same substitution, when x =3, y = 4
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