In previous lessons of solving linear equations and systems, you have learned that each linear system has only one solution. In this upcoming section, you will discover that there are more than one type of linear systems unlike the previous ones.

Examples of Linear Systems

a. 2x+y=3 equation 1

b. 2x+3y=6 equation 2

a. y= - 2x +3 revised equation 1

b. y= - 2x +4 revised equation 2

 

Possibilities of Linear Systems:

Graph one shows many solutions, graph two shows one solution, and graph three shows no solution.

 

Examples of Linear Equations:

To solve these you need to: 1) Multiply one of the equations by a number that will make one of the numbers in the equation opposite to one in the other eqaution. (opposites are negative with postive, they will cancel out)

2) Cancel out the opposites and solve the equation.

3) Depending on the answer, you can conclude whether their is one solution, many solutions, or no solution.

1. ( 2x + 3y = 8) revised : ( -6x - 9y = - 24)

( 6x + 9y = 24) revised: ( 6x + 9y = 24)

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solution: 0x + 0y = 0 ( at the top ^ they cancel each other out)

2. ( x = 4y + 21) ( revise the solution to where all of equation or some of it cancels out.)

( 3x - 12y = -21) ( notice how the - and + 21 will cancel eachother out)

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revised solution: y = 1/4x + 21/12 no solution, lines on graph are parallel

 

 

After solving the solution to the linear systems you can create and graph to match the answer. The graphs will look similiar to the examples at the top of the page. Hopefully no you can figure out other ways to solve linear systems.