7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

7.4 Solving a System of Linear Equations Using Substitution

Graphing is a somewhat reliable however tedious method to solving linear systems.There are two other methods that we use, especially when graphing is not an option.

The first of the two is called substitution

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Consider the following linear system:

2x + y = 5y = -x + 3

**We can transform two linear systemsinto one! Taaaaa-daaaaaa!

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

As mentioned before, we use substitution to turn two equations with two unknowns, it's one equation, one unknown.

With substitution, you're looking for "easy" equations, ones where the algebra required is simplistic.

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Example 1.3x + 4y = -4x + 2y = 2

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Example 2. Nuri invested $2000, part at an annual interest rate of 8% and the rest at an annual interest rate of 10%. After one year, the total interest was $190. How much money did Nuri invest at each rate?

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

The following two systems are called equivalent linear systems (why?):

System A System B

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Example 3. Solve this linear system by substitution.

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

7.5 Using Elimination to Solve a System of Linear Equations

Substitution is useful when one of the equations in a system is very easy to algebraically manipulate. In other situations, we use the idea of equivalent equations to solve a system.

The thing that we want to do is eliminate a variable by adding or subtracting linear systems.

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

7.5 Using Elimination to Solve a System of Linear Equations

Substitution is useful when one of the equations in a system is very easy to algebraically manipulate. In other situations, we use the idea of equivalent equations to solve a system.

The thing that we want to do is eliminate a variable by adding or subtracting linear systems.

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Consider the following linear system:

3x - 4y = 75x - 6y = 8

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Example 1. Use an elimination strategy to solve this linear system.

7.4 & 7.5 Solving Systems Algebraically

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June 10, 2014

Example 2. Solve the linear system (note - you may need to do elimination each variable... we'll see why)

2x + 3y = 85x - 4y = -6