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1.3.3.html by Meg Cheng-Campbell Per. 1

®When you solve an equation, know the 2 special cases for:

No Answer and All real numbers.

-Graphically, it has to do with parallel lines and lines that are the exact same line.

-When you solve Algebraically, you get either an untrue statement like 2=5 or one that is true like 4=4.

-If the result of a linear equation does not balance our (ex: 7=2) then there is “no solution”

-If the result balances out correctly (ex: 1=1) then the answer is “all real numbers”

Example #1: 3a+2=3a+3

a) Solve Algebraically:

3a+2=3a+3 _{subtract 2 from both sides}

3a=3a+1 _{subtract 3a from both sides}

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Answer = No Solution

b) Solve Graphically:

1è graph both sides of the original problem separately

2è notice that they are parallel and therefore the answer is “No Solution”

Example #2: -3+4y+6=-4y+8y+3

a) Solve Algebraically:

-3+4y+6=-4y+8y+3 _{add 3 to both sides}

4y+6=-4y+8y+3+3 _{add 3+3}

4y+6=-4y+8y+6 _{add 4y to both sides}

4y+4y+6=8y+6 _{add 4y+4y}

8y+6=8y+6 _{subtract 8y from both sides}

6=6

Answer = All Real Numbers

b) Solve Graphically:

1è graph both sides of the original problem separately

2è notice that they are the same line and therefore the answer is “All Real Numbers”

Two lines on top of each other

→Now you try:

Solve algebraically or graphically

Possible Answer