SOLUTION: You solved a linear system and got the equation -6 = 0. How many solutions does the system of equations have? (Please Explain) A. No solution B. Infinitely many solutions C.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: You solved a linear system and got the equation -6 = 0. How many solutions does the system of equations have? (Please Explain) A. No solution B. Infinitely many solutions C.      Log On


   

Question 1012365: You solved a linear system and got the equation -6 = 0. How many solutions does the system of equations have? (Please Explain)

A. No solution
B. Infinitely many solutions
C. Exactly 1 solution
D. 2 solutions
Found 2 solutions by rothauserc, Theo:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
-6 = 0 says that 0 is equal to a non-zero number which is a contradiction.
The answer is A.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
-6 = 0 means no solution.

that's because the statment is false.

if you got something like 1 = 1, then the statement will be true and you will get an infinite number of solutions.

two simple problems to illustrate.

first equation is 5x + 10y = 15
second equation is 10x + 20y = 30

multiply both sides of the first equation by 2 and leave the second equation as is to get:

10x + 20y = 30
10x + 20y = 30

when you subtract the second equation from the first, you will bget 0 + 0 = 0 which results in 0 = 0.

since this equation is true, you will get an infinite number of solutions and any value of x or y in the first equation will also solve the second equation as well.

if you graphed these two equations, you will see that they are identical.

if you converted them to slope intercept form and simpklified, you will see that they are the same equation.

now look at:

5x + 10y = 15
10x + 20y = 45

multiply the first equation by 2 and leave the second equation as is to get:

10x + 20y = 30
10x + 20y = 45

subtract first equation from second equation to get 0x + 0y = 15 which results in 0 = 15.

this equation is not true, therefore there is no solution.

if you graphed both these equations, you would see that they are parallel.

since they are parallel lines, they will never intersect therefore there is no solution common to both.

here's a graph of all 3 equations.

$$$