Question

How many solutions does this system of equation have?
y=5x+7 and 3y-15x=18

Answer 1

\(\color{#000000 }{ \displaystyle y=5x+7\quad \Longrightarrow \quad y-5x=7 }\)


\(\color{#000000 }{ \displaystyle 3y-15x=18\quad \Longrightarrow \quad y-5x=6 }\)
divide
the eq
by 3

Answer 2

divide the 2nd eqn by 3 then rearrange to the form y =
now compare eqn 1 with eqn 2

Answer 3

OK, thanks but only 3y -15x =18?

Answer 4

Is it possible that \(\color{#000000 }{ \displaystyle y-5x }\) is 6 and 7 at the same time?

Answer 5

BUt it seems confusing...

Answer 6

What seems confusing?

Answer 7

Like, the y-5x= 6 & 7

Answer 8

\(\color{#000000 }{ \displaystyle y-5x }\)
is jut a number (EXCEPT, that it is an unknown number - you don't know what it is equivalent to).

Answer 9

So would the answer be 2 solutions? Im so confused.

Answer 10

So, if it comes out that
\(\color{#000000 }{ \displaystyle (y-5x)=7 }\) (from 1st equation)
and
\(\color{#000000 }{ \displaystyle (y-5x)=6}\) (from 2nd equation)

Answer 11

would that be possible?

Answer 12

Could same number be equal to 6 and equal to 7 (all at once)?

Answer 13

No.

Answer 14

No solution

Answer 15

So would that mean it needs to be 2? Or could there be more?

Answer 16

Wait, no, so not 2. Yea no solution, its not possible.

Answer 17

yes

Answer 18

You're right/

Answer 19

The same number could not equal two different numbers with both,

Answer 20

equations

Answer 21

\(\color{#000000 }{ \displaystyle (y-5x)=7 }\) (from 1st equation)
\(\color{#000000 }{ \displaystyle (y-5x)=6 }\) (from 2nd equation)

For this to be possible we would need to have
\(\color{#000000 }{ \displaystyle 6=7 }\)

Answer 22

Yes, so no solution. Thanks!

Answer 23

and yes, must be that system will not have a solution...

Answer 24

yw

Answer 25

No solution because the lines are parallel to each other.
{ y=7+5 x, y=6+5 x }