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# Solving Linear Systems - PowerPoint PPT Presentation

Solving Linear Systems. The solution of a system of equations in two variables is an ordered pair ( x,y ) that satisfies each equation. Consistent – means that there is at least one solution Inconsistent - if there are no solutions then the system is inconsistent The two lines are parallel

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## PowerPoint Slideshow about ' Solving Linear Systems' - zuri

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Presentation Transcript

• The solution of a system of equations in two variables is an ordered pair (x,y) that satisfies each equation.

• Consistent – means that there is at least one solution

• Inconsistent - if there are no solutions then the system is inconsistent

• The two lines are parallel

• Dependant – a consistent system with infinitely many solutions

• The two lines are on top of each other

• Independent – a consistent system with exactly ONE solution

• **All this vocabulary only applies to linear systems

• Graph each of the below and classify the system as consistent and independent; consistent and dependant or inconsistent:

• Examples:

• 1) Solve for y (put in y=mx+b form) to make graphing easier

• 2) Graph each line by using slope intercept form:

• Find the y-int

• Count off the slope

• 3) Look for places that the graphs intersect and list these as solutions

• 4) Verify solutions algebraically by plugging in each part of the ordered pair solutions

• Word Problems can be solved in the following manner

• Create a linear model for the problem

• Solve each linear equation for the same thing (what we do when we solve for y in the earlier problems) then set these equations equal to each other.

• Examples: pg. 9 29 and 33

• Algebraically – solve for one variable, set equal and find solution

• Graphically – graph and look for intersection points

• Simple Examples:

• Solve: a) 2x=8

• b) x-5=2

• c) 2x+5=x-1

• Just like linear equations are solved by looking for the places that their graphs intersect; non-linear systems are also solved by finding intersection points.

• Examples will be shown later…..

• Solutions or intersection points can be found algebraically by setting each equation equal to each other.

• Example – find the solution(s) for the below set of functions

• Find the solution(s) for the following set of functions algebraically:

• Example 1:

• Use a graph to identify ordered pair solution(s) for the following set of equations

Identify Solutions

Check Algebraically

• Example 2:

Heather and Amanda each improved their yards

by planting hostas and geraniums. They bought

their supplies from the same store.

Heather spent \$187 on 12 hostas and 13 geraniums.

Amanda spent \$109 on 4 hostas and 11 geraniums.

What is the cost of one hosta and the cost of one geranium?