Help your students prepare for their Maths GCSE with this free simultaneous equations worksheet of 33 questions and answers
Simultaneous equations are pairs of equations with two unknowns. There are different types of simultaneous equations that we can solve. When both equations are linear equations we can use the elimination method. Here, we need to compare the coefficients of the variables and find ones that match. One or both of the equations will often need to be multiplied by an integer so that the coefficients of one of the variables is the same in both equations. The equations can then be added or subtracted to eliminate one of the variables. Once one of the variables is found, we can then substitute it back into one of the equations in order to find the second variable.
We can also solve linear simultaneous equations by using the substitution method where one of the equations is substituted into the other equation. We can then solve the equation to work out one of the variables and then substitute it back into one of the original equations to find the value of the second variable.
We can also solve a pair of simultaneous equations where the first equation is linear and the second equation is quadratic by using the substitution method. The linear equation is used to make a substitution into the nonlinear equation.
Solving simultaneous equations can also be used to find the point of intersection of straight lines and curved lines.
Looking forward, students can then progress to additional simultaneous equations worksheets on to more algebra worksheets, for example a simplifying expressions worksheets or an inequalities worksheet.
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