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ALGEBRA

SIMULTANEOUS EQUATIONS

Solving Simultaneous Equations

Sometimes, equations have more than one unknown quantity. When this occurs, we must solve them simultaneously. For example, if I know that two cups of tea and three cups of coffee cost £2.50, and I also know that five cups of tea and four cups of coffee cost £4.20, I can set up two equations and hence find the price of one cup of tea and one cup of coffee.  

Prior knowledge

Key Terms

  • Simultaneous equation: Two or more equations that are true at the same time. 

  • Variable: A value that can "vary", i.e. change. Simultaneous equations have more than one variable. 

  • Solving: Finding unknown values within an equation.

Quadratic Simultaneous Equations

Simultaneous equations can be quadratic. This is where at least one of the equations has a squared term. When we have quadratic simultaneous equations, the method for solving linear simultaneous equations does not quite work. Luckily, there is another trick we can use and so in this section, we look at the method for doing so.

Key Terms

  • Quadratic: an expression where the highest power term is a squared term.

  • Simultaneous equations: Two or more equations that are true at the same time. 

Solving Simultaneous Equations Graphically

The final method for solving simultaneous equations is to do so graphically. This involves sketching the graphs of the linear equations and finding the points where the lines intersect. At that point of intersection, both equations are simultaneously true. 

Prior knowledge

  • Sketching straight-line graphs

  • solving simultaneous equations 

  • Rearranging equations 

Key Terms

  • Linear graph: A straight-line graph. 

  • Intersection: The point where two lines meet. 

  • Simultaneous equation: Two or more equations that are true at the same time. 

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