Solving Systems of Equations

​y = 3x - 7

y = 7x - 3

Solving Systems of Equations

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Thank you very much = Donke shoen

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Thank you very much = Obrigado

Solving Systems of Equations

​y = 3x - 7

y = 7x - 3

Solving Systems of Equations

Methods We Have Used to Solve Systems of Equations

• ​Substitution

• Elimination

• ​Graphing

Lets take a look!

One Solution looks like..

​

• ​Two lines intersect at one point

• ​Solution is an ordered pair (x,y)

No Solution Looks Like..

• These lines will never intersect

• ​Parallel Lines

• ​Same slopes different y-intercepts

Infinite Amount of Solutions Looks Like..

Lines on top of each other

• ​They are the same line when simplified or written in slope-intercept form

Substitution

• Used when we we have a single variable isolated.

• The coefficient of the isolated variable should be 1.

• Replace the variable in 1 equation, with the isolated variable from the other equation.

• Find the other solution by replacing the unknown variable with the newly found variable.

Elimination

• Best when the equation is in Standard Form

• Look for matching coefficients and variables that OPPOSITE signs

• If needed you can multiply by a constant to make variables match and be opposite

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Solving by Substitution

Steps 1 & 2

Solving by Substitution

Steps 3 & 4

The solution is (42,-12)

Solving by Substitution

Example 2

Solving by Elimination

Steps 1 & 2

Solving by Elimination

Steps 3/4 & 5/6

The solution is (2,4)

Solving by Elimination

Example 2