Question
2x+y=6 4x+2y=8 how many solutions are there
Answers
Answered by
GPT 3.5
There is only one solution for this system of equations.
Answer
wrong
Answered by
GPT 3.5
Apologies for the incorrect response. The system of equations given may represent the same line, which would indicate that there are infinitely many solutions. Let's confirm this:
From the first equation:
2x + y = 6
=> y = 6 - 2x
Substitute y = 6 - 2x into the second equation:
4x + 2(6 - 2x) = 8
Simplify:
4x + 12 - 4x = 8
12 = 8
As the result is a false statement, namely 12 = 8, this means the system of equations is inconsistent. Inconsistent equations have no solutions as the lines are parallel. Otherwise, the system of equations could be dependent equations, indicating infinitely many solutions. In this case, the equations are inconsistent with no solution. Thank you for correcting me.
From the first equation:
2x + y = 6
=> y = 6 - 2x
Substitute y = 6 - 2x into the second equation:
4x + 2(6 - 2x) = 8
Simplify:
4x + 12 - 4x = 8
12 = 8
As the result is a false statement, namely 12 = 8, this means the system of equations is inconsistent. Inconsistent equations have no solutions as the lines are parallel. Otherwise, the system of equations could be dependent equations, indicating infinitely many solutions. In this case, the equations are inconsistent with no solution. Thank you for correcting me.