exam Maths Puzzle Numerical Ability

how can one determine if a word problem can be solved using the Quadratic Equation and why one can determine that?
Thank you so much!!

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exam Other Question

Find an equation in standard form for a line through P(-3, 2) and parallel to the line containing (2,3) and (1,-2). What is the equation? Solve the following system of linear equations using the elimination (addition) method.

5x-2y=4
3x+3y=-6 Stimultaneous Solution = (__,__)