Question

Solve x − 2y = 6
3x − 6y = 18

(2, −2)

(3, negative three halves)

No Solutions

Infinitely Many Solutions

Answer 1

turn into y = mx + b form
x − 2y = 6

Answer 2

Solve by sub
\(\large x=2y+6\)
\(\large 3x-6y=18\)
\[\LARGE 3(2y+6)-6y=18\]
Distribute and solve.

Answer 3

then work from there

Answer 4

divide the 3rd equation (each thing in it) by 3. it will turn into the 1st equation.

Answer 5

._.

Answer 6

x - 2y = 6
- x -x

-2y = -x +6
/-2 /-2

>>>>>>y = x/2 - 3<<<<<<

Answer 7

What ?

Answer 8

Yes, that's correct — the solution is the equation of a line. What does that mean about the number of solutions?

Answer 9

If you solve it by sub you get.. \(\large 18=18\)
Do you know what that means? >_>

Answer 10

y = mx + b form:
3x − 6y = 18
-3x -3x

-6y = -3x + 18
/-6 /-6

>>>>>>y = 1/2x - 3<<<<<
thats our second equation^^

Answer 11

y = x/2 - 3
y = 1/2x - 3

Since they are on the same line ~ they can go on & on so: Infinitely Many Solutions

Answer 12

@AyyoDutches

Answer 13

btw.. \(\LARGE \frac{x}{2} \neq \frac{1}{2x}\)

Answer 14

yeah, that's sloppy writing, should be y = (1/2)x-3

Answer 15

luigi, if x=1, then yes ;)

Answer 16

Why couldn't you guys just use substitution? ლ(ಠ_ಠლ)
And I see what you did there Solomon xD

Answer 17

(*_*)

Answer 18

>Confused<

Answer 19

@AyyoDutches You have two equations which turn out to represent the same line. As any point that is on both lines is a solution, that means that any point on either line is a solution, and there are infinitely many points on a line, so there are infinitely many solutions.

Answer 20

~ the answer is Infinitely Many Solutions ~ because of the explanations above XD

Answer 21

If you had two parallel lines, you would have no solutions. An example would be

y = x+5
y = x+6

same slope, so parallel, but no point satisfies both equations, so there are no solutions

Answer 22

most often when solving such problems, the lines intersect (once only, if straight lines), and thus the point of intersection is the only point that satisfies all of the equations in the system, giving you just one solution