#NumberAndAlgebra #Path #Adv >[!info]- [Equations C (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa587a4c87) >- MA5-EQU-P-02 solves linear equations of more than 3 steps, monic and non-monic quadratic equations, and linear simultaneous equations ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ------------------------------------------------------ | --------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------- | | [[Stage 4/Linear Relationships\|Linear Relationships]] | - point of intersection is the simultaneous solution | - solving simultaneous equations graphically | | [[Algebraic Techniques C]] | - simplifying algebraic fractions<br>- factorising non-monic quadratic trinomials | - solving equations with two or more fractions<br>- solving non-monic quadratic equations | | [[Equations B]] | - solving monic quadratic equations | - solving non-monic quadratic equations | | [[Indices C]] | - operations with surds | - quadratic formula | ## [[Solve linear equations involving algebraic fractions and equations of more than 3 steps.pdf]] - Solve linear equations involving more than 3 steps - Solve equations that involve 2 or more fractions ## [[Rearrange literal equations.pdf]] - Change the subject of a formula ## [[Solve quadratic equations using a variety of methods.pdf]] - Solve equations of the form $ax^2+bx+c=0$ by factorisation and by completing the square - Apply the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to solve quadratic equations - Apply the most appropriate method to solve a variety of quadratic equations - Use substitution to verify solutions to quadratic equations - Identify whether a given quadratic equation has real solutions, and if there are real solutions, whether or not they are equal - Solve quadratic equations resulting from substitution into formulas in various contexts - Model and solve word problems using quadratic equations in various contexts - Solve equations that are reducible to quadratics ## Solve linear simultaneous equations, both algebraically and graphically - Solve linear simultaneous equations by finding the point of intersection of their graphs - Solve linear simultaneous equations using algebraic techniques including substitution and elimination methods - Model and solve word problems using simultaneous equations and interpret their solutions - Describe an identity as an equation that is true for all values of the pronumeral and relate the identity to coincident lines - Describe a contradiction as an equation that has no solutions and relate the contradiction to parallel lines