
Mathematics (secondary)  Secondary/KS4/GCSE (age 1415 yrs)
Q: The equation of line A is (x)^2 + 11x + 12 = y  4, while the equation of line B is x  6 = y + 2. Find the coordinate(s) of the point at which lines A and B intersect.
While this question may seem complicated, this question is simply asking you to solve the equations of these two lines as simultaneous equations. Line A: x2 + 11x + 12 = y  4 > x2 + 11x + 16 = y; Line B: x  6 = y + 2 > x  8 = y. At the coordinate(s) at which lines A and B intersect, x2 + 11x + 16 = x  8. If you bring all the x's in the equation above to the same side: x2 + 10x + 24 = 0, which can also be written as: (x + 6)(x + 4) = 0. Solving this equation for x: x + 6 = 0 (x =  6) AND x + 4 = 0 (x =  4)When x =  6, y = ( 6)  8 =  14 AND when x =  4, y = ( 4)  8 =  12... Therefore lines A and B cross at two points: ( 6, 14) and (4, 12)
Maria
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Maria
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Literae Humaniores (Bachelors)  Wadham College, Oxford University