## ashleysmith 3 years ago How do you determine if linear equations are parallel without graphing like 2x + 2y=4 3x +y=3

1. lgbasallote

simplify the equations as much as possible for example 2x + 2y = 4 i can divide all terms by 2 and simplify it to x + y = 2 got that part?

2. ashleysmith

Yeah , after you simplify it how do you know if it's parallel or perpendicular

3. lgbasallote

you look at the next equation (note that it has to be simplified as much as possible too) our first equation is x + y = 2 if our second equation is also x+y = c <---c is a constant (which means it is any number)..the important thing is the x+y if the left sides of BOTH equations look EXACTLY the same then they are parallel got it?

4. ashleysmith

Yeah what if the slope is the same ?

5. lgbasallote

when the slopes are the same then they are parallel

6. lgbasallote

to know if it is perpendicular...simplify the equations again...then put it in the form ax + by = c so you can see it better now when the left sides of BOTH equations look the same BUT the only difference is the sign of x, then they are perpendicular

7. lgbasallote

would you like an example?

8. ashleysmith

Sure:)

9. lgbasallote

okay... 2x + 2y = 4 3y = 9 - 3x the first step is to simplify both equations..i divide the first equation by 2 and get x + y = 2 now i divide the second equation by 3 (since it is common to all terms) y = 3 - x now the second step is to put in the form ax + by = c the first equation is already in that form so no worries the second equation would then look like x + y = 3 now let us compare (1) x + y = 2 (2) x + y = 3 what can you say?

10. ashleysmith

Parallel!!

11. ashleysmith

Thank you so much