Simultaneous Equations

Types- (2 equations) Linear Linear & Non Linear NonLinear

Methods Algebraic Substitution Elimination Graphical Matrix

2 Linear Equations Graphical Method Algebraic Methods Solutions Substitution Elimination Solutions

Substitution Combine the two equations by substituting one into the other 1. Make one of the variables the subject of one of the equations 2. Substitute the subject into the other equations The result is that we end up with one equation with one unknown which we can solve for, then: 3. Find the other variable by substituting into a previous equations

Substitution Solve: 𝑥+𝑦=7 𝑥−𝑦=3

Substitution Solve: 3𝑥+𝑦=18 2𝑥−𝑦=7

Substitution Solve: 𝑦=2𝑥−1 𝑦=𝑥+3

Substitution Solve: 3𝑦+4𝑥=2 𝑥−3𝑦=8

Substitution Solve: 4𝑥+2𝑦=5 3𝑥+6𝑦=6

Substitution Solve: 3𝑥−5𝑦=−16 5𝑥+6𝑦=45

Elimination Combine the two equations by adding/subtracting the two equations in such a way that one of the variables is eliminated 1. Make one of the variables have the same coefficient 2. Add ( if the signs are different); subtract (if the signs are different) to eliminate that variable The result is that we end up with one equation with one unknown which we can solve for, then: 3. Find the other variable by substituting into a previous equations

Elimination Solve: 𝑥+𝑦=7 𝑥−𝑦=3

Elimination Solve: 3𝑥+𝑦=18 2𝑥−𝑦=7

Elimination Solve: 3𝑦+4𝑥=2 𝑥−3𝑦=8

Elimination Solve: 4𝑥+2𝑦=5 3𝑥+6𝑦=6

Elimination Solve: 3𝑥−5𝑦=−16 5𝑥+6𝑦=45

Elimination Solve: 2𝑥−5𝑦=−8 −3𝑥−2𝑦=−26

Linear & NonLinear Graphical Method Algebraic Methods Solutions Substitution ***Elimination Solutions