GCSE Maths (Edexcel)

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Solving Quadratic Simultaneous Equations

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Algebra Solving Equations and Inequalities

Solving Quadratic Simultaneous Equations

7:11 Quadratic Simultaneous Equations
Spec A19
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  • Quadratic simultaneous equations can be solved using substitution and solving the resulting quadratic in one variable
  • Each solution to the pair of equations will give us a value of x and a value of y that satisfy both equations
  • Substitution is generally used to solve simultaneous equations
  • Once we find the x values that solve the equations, we can substitute them back into the original equations to find the y values
  • When there is a linear equation and a quadratic equation, there can be up to two solutions
  • The x and y values correspond to the coordinates on the graph where the straight line intersects the quadratic curve
  • To solve quadratic equations, we can use factorization, the quadratic formula, or completing the square
  • The factor pair that adds to the coefficient of the linear x term is used to write the factorized quadratic equation
  • The solutions to the simultaneous equations are found by deducing which values of x make each bracket zero
  • The y values of the solutions are found by substituting the x values back into the linear equation

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