Systems of Equations and Inequalities

Advanced MathChapter 9

Linear and Nonlinear Systems of Equations

Advanced Math 9.1

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System of equations

• Two or more equations in two or more variables.• We must find the values of the variables that

make all the equations true – the solution.

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Substitution Method1. Solve one of the equations for one variable

in terms of the other.2. Substitute in the other equation to get and

equation in one variable.3. Solve the equation.4. Back-substitute to find the other variable.5. Check your solution.

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Examples• Solve each system of equations.

3 2 162 0

x yxx y

6 3 4 02 4 0

x yx y

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Solving graphically

• Can help find out how many solutions there are – how many times graphs cross

• Can approximate solutions– You still need to check answers to find exact

ones unless it says approximate to a certain number of decimal places.

• Note: calculators only graph y=, so must get it into that form first.

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Example• Solve the system graphically. Round your

answers to the nearest hundredth.

3 2 6

ln 1x y

y x