Question

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

Answer 1

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?

Answer 2

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

Answer 3

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?

Answer 4

Yeah what if the slope is the same ?

Answer 5

when the slopes are the same then they are parallel

Answer 6

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

Answer 7

would you like an example?

Answer 8

Sure:)

Answer 9

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?

Answer 10

Parallel!!

Answer 11

Thank you so much