SOLUTION: For what values of c will the system have: infinitely many solution 1) 2x - 6y = c 6x - 18y = 30 2)no solution x + 2y = 6 cx

SOLUTION: For what values of c will the system have: infinitely many solution 1) 2x - 6y = c 6x - 18y = 30 2)no solution x + 2y = 6 cx - 4y = 8 How do you do these qu

Question 184605: For what values of c will the system have:
infinitely many solution
1) 2x - 6y = c
6x - 18y = 30
2)no solution
x + 2y = 6
cx - 4y = 8

How do you do these questions? Can you explain how?
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
infinitely many solution
1) 2x - 6y = c
6x - 18y = 30
infinitely many solution means the two 'lines' are really the same line
the second line above has two terms that are exactly 3 times the terms of the fisrt line (6x = 3*2x and -18y = 3 *(-6y)) so if c is 3*30, then the two lines are really the same line.
2)no solution
x + 2y = 6
cx - 4y = 8
No solution occurs when the 'answer' is something that can't happen
So let's double the first line to get
2x + 4y = 12
Now add the second line to it
2x + 4y = 12
cx -4y = 8
----------
(2+c)x = 20
any c that that makes (2+x) a non-zero number will result in an x that 'works'. However, if c = -2, then we get
(0*x) = 20
0 times anything is 0, so that yields
0 = 20
0=20 is impossible, so is c = -2 then ther eis no solution.,
make sense?
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