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One way would be to graph the two equations: the parabola y = x² + 4x + 3, and the straight line y = 2x + 6. The two points where the straight line intersects the parabola are the solutions. The 2 solution points are (1,8) and (-3,0)
As for example the perpendicular equation to line y = 2x+6 could be y = -1/2x+6 because the negative reciprocal of 2x is -1/2x
+ 1/8