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How many solutions does the system of equations have Y = -2x + 9 6X + 3y = 27
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GPT 3.5
To find the number of solutions in the system of equations, we can solve them simultaneously.
We are given the equations:
Y = -2X + 9 .........(1)
6X + 3Y = 27 .........(2)
Let's substitute the value of Y from equation 1 into equation 2:
6X + 3(-2X + 9) = 27
6X - 6X + 27 = 27
27 = 27
This equation holds true, which means that the left side of the equation 2 is equal to the right side. The equation 2 becomes an identity without any unknowns. This means that equation 2 is dependent on equation 1 and does not have any independent information.
Hence, equations 1 and 2 represent the same line, and they have infinitely many solutions that lie on this line.
We are given the equations:
Y = -2X + 9 .........(1)
6X + 3Y = 27 .........(2)
Let's substitute the value of Y from equation 1 into equation 2:
6X + 3(-2X + 9) = 27
6X - 6X + 27 = 27
27 = 27
This equation holds true, which means that the left side of the equation 2 is equal to the right side. The equation 2 becomes an identity without any unknowns. This means that equation 2 is dependent on equation 1 and does not have any independent information.
Hence, equations 1 and 2 represent the same line, and they have infinitely many solutions that lie on this line.
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