Quadratic Simultaneous Equations Worksheet

Quadratic simultaneous equations at a glance

Quadratic simultaneous equations are pairs of equations where one is one quadratic and one linear.

To solve quadratic simultaneous equations we can use the elimination method in a similar way to solving linear simultaneous equations.  We need to substitute the linear equation into the quadratic (non-linear) equation which may have one variable which is squared, or both variables which are squared. This quadratic equation is then solved and two solutions are found. Both of these solutions need to be substituted one at a time into the first equation or the second equation to calculate two pairs of solutions. 

In order to answer these questions, a strong understanding of solving quadratic equations by factorising or using the quadratic formula is required. The final answers can be given as integers, fractions, decimals or surds as required.

Quadratic simultaneous equations can be used to find where a line intersects a parabola or a circle. This can be extended to calculating the equation of a tangent to circle.

Looking forward, students can then progress to additional simultaneous equations worksheets on to more algebra worksheets,  for example a simplifying expressions worksheet, or an inequalities worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.