# Solving Linear Equations

Students learn how to solve an equation using the balance method and trial and improvement.  As learning progresses they are taught how to form and solve a pair of simultaneous equations from known geometrical facts and real life problems.  This unit takes place in Year 9 Term 5 and leads on to solving and representing inequalities and inequations.

##### Prerequisite Knowledge
• Use simple formulae
• Generate and describe linear number sequences
• Express missing number problems algebraically
• Find pairs of numbers that satisfy an equation with two unknowns
• Use and interpret algebraic notation
• Simplify and manipulate algebraic expressions by:
• collecting like terms
• multiplying a single term over a bracket
##### Success Criteria
• Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)
• Solve two simultaneous equations in two variables algebraically;
• Find approximate solutions to simultaneous equations in two variables using a graph;
• solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)
• Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution.
##### Key Concepts
• To solve an equation is to find the only value (or values) of the unknown that make the mathematical sentence correct.
• For every unknown an equation is needed.
• Students need to have a secure understanding of adding and subtracting with negatives when eliminating an unknown.
• Coefficients need to be equal in magnitude to eliminate an unknown
##### Common Misconceptions
• Students can forget to apply the same operation to both sides of the equation therefore leaving it unbalanced.
• Students often struggle knowing when to add or subtract the equations to eliminate the unknown. Review addition with negatives to address this.
• Equations need to be aligned so that unknowns can be easily added or subtracted. If equations are not aligned students may add or subtract with non like variables.
• Students often try to eliminate variables with their coefficients being equal.

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