SOLUTION: A linear equation 3x +4y =7 has a unique solution. state true or false. Justify your answer.

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Question 944515: A linear equation 3x +4y =7 has a unique solution. state true or false. Justify your answer.
Found 2 solutions by rothauserc, Edwin McCravy:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
False, any point on the line satisfies the equation
3x + 4y = 7
4y = -3x + 7
y = -3x/4 + 7/4
Below is the graph of the linear equation
graph%28300%2C200%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2F4+%2B+7%2F4%29

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A linear equation 3x +4y =7 has a unique solution. state true or false. Justify your answer.
False.

3(1) + 4(1) = 7
      3 + 4 = 7
          7 = 7
So (x,y) = (1,1) is one solution.


3(-7) + 4(7) = 7
    -21 + 28 = 7
           7 = 7
So (x,y) = (-7,7) is another solution.


3(-3) + 4(4) = 7
     -9 + 16 = 7
           7 = 7
So (x,y) = (-3,4) is another solution.


3(5) + 4(-2) = 7
      15 - 8 = 7
           7 = 7
So (x,y) = (5,-2) is another solution.


3%282%2F3%29+%2B+4%285%2F4%29+=+7
       2 + 5 = 7
           7 = 7
So (x,y) = %28matrix%281%2C3%2C++2%2F3%2C%22%2C%22%2C5%2F4%29%29 is another solution.



There are an infinite number of solutions.

Edwin