Question

How many solutions are there to the following system of equations?

3x – 9y = 0
–x + 3y = –3

Answer 1

multiply the second equation through by 3, then add the two equations together, see what you get from that

Answer 2

Or from inspection, you can see that the coefficients on the first equation, are 3 times the coefficients in the second,

If the coefficients on X and Y are scalar multiples of one another, you have parallel lines

Answer 3

If you put them in y = m*x + b form, you will see they both have the same slope m, but different y intercepts, b, parallel lines.

Answer 4

Solutions are the intersection points (x,y). How many solutions would two parallel lines have then?

Answer 5

Sooo does that mean there's no solution since they're parallel?

Answer 6

that is right

Answer 7

parallel line - no solution
intersecting lines - One Solution
overlapping lines - Infinite Solution

Answer 8

Notice if you try and solve these:

3x – 9y = 0
–x + 3y = –3 multiply second by 3
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3x - 9y = 0
-3x+9y = -9 add the two equations together
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0x + 0y = -9

0 = -9 ?? FALSE Statement, NO Solutions

Answer 9

sorry reload page

Answer 10

OOH okay thank you!!