Simultaneous Equations (Edexcel IGCSE Maths A (Modular))

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  • What are linear simultaneous equations?

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  • What are linear simultaneous equations?

    Linear simultaneous equations are equations with two unknowns (say x and y) where the terms have variables with no powers higher than 1 (so no x squared, y squared, x y, etc.).

    E.g. 4 x minus 11 equals y and 3 x plus 4 y equals 32.

  • What is the elimination method for solving simultaneous equations?

    The elimination method completely removes one of the variables, x or y, from the simultaneous equations by adding or subtracting the equations (after multiplying them by suitable constants if necessary).

    E.g. For the pair of simultaneous equations 2 x plus 3 y equals 3 and 6 x minus 5 y equals 23:

    1. Multiply one equation to make the coefficient of one variable the same, Multiply 2 x plus 3 y equals 3 by 3 to get 6 x plus 9 y equals 9.

    2. Add or subtract the equations to eliminate a variable, negative 14 y equals 14

    3. Solve to find one variable, y equals negative 1.

    4. Substitute into one of the equations and solve for the other variable, x equals 3.

  • What is the substitution method for solving simultaneous equations?

    The substitution method involves rearranging one equation to make one variable (x or y) the subject, and then substituting this expression into the other equation to eliminate that variable.

    E.g. For the pair of simultaneous equations 3 x plus y equals 7 and 2 x plus 1 equals 5 y:

    1. Rearrange the first equation to make y the subject, y equals 7 minus 3 x.

    2. Then substitute the expression for y into the second equation, 2 x plus 1 equals 5 open parentheses 7 minus 3 x close parentheses.

    3. Solve for x, x equals 2.

    4. Substitute the value for x into one of the equations and solve for y, y equals 1.

  • How can you use a graph to solve linear simultaneous equations?

    To solve linear simultaneous equations using a graph, plot both equations on the same set of axes and find the point of intersection.

    The x- and y- coordinates of that point give the solutions for x and y.

  • True or False?

    It is a good idea to always check that your final solutions satisfy the original simultaneous equations.

    True.

    It is a good idea to always check that your final solutions satisfy the original simultaneous equations.

  • What are quadratic simultaneous equations?

    Quadratic simultaneous equations are simultaneous equations where at least one equation contains a squared term (x squared or y squared or x y).

  • How is the substitution method used to solve quadratic simultaneous equations?

    To use substitution to solve quadratic simultaneous equations:

    • Rearrange the linear equation to make one variable the subject.

    • Substitute this expression into the quadratic equation.

  • True or False?

    When giving your final answer for a quadratic simultaneous equations question, you must indicate clearly which x and y values go together.

    True.

    When giving your final answer for a quadratic simultaneous equations question, there will typically be two pairs of solutions.

    You must indicate clearly which x and y values go together.

  • True or False?

    With quadratic simultaneous equations, if the resulting quadratic has no solutions after substitution, then on a graph showing both equations the line does not intersect with the curve.

    True.

    With quadratic simultaneous equations, if the resulting quadratic has no solutions after substitution, then on a graph showing both equations the line does not intersect with the curve.

  • With quadratic simultaneous equations, what does it mean on a graph if the resulting quadratic has only one unique solution after substitution?

    With quadratic simultaneous equations, if the resulting quadratic has only one unique solution after substitution, it means that on a graph showing both equations the line only touches the curve at one point.

  • True or false?

    You can take the square root of both sides of the equation  x squared plus y squared equals 25  to turn it into  x plus y equals 5.

    False.

    You cannot take the square root of both sides of the equation x squared plus y squared equals 25 to turn it into x plus y equals 5. This is a common mistake made by students on the exam.

    The square root of 25 is 5 (or negative 5), but the square root of x squared plus y squared is not x plus y.

    If you take the square root of both sides, you get square root of x squared plus y squared end root equals 5, but that isn't going to help you solve the equation.