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Ewan_C
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[Solved] 3x4 system of equations
Consider the following system of three equations in x, y and z.
2x + 4y + 5z = 17
4x + ay + 3z = b
8x + 7y + 13z = 40
Give values for a and b in the second equation that make this system consistent, but with an infinite set of solutions.
I found the answers a= -1, b=6 easily enough. I was told by my teacher that if a system of three equations has infinite solutions, one of the equations can be found from the other two. I multiplied equation 1 by 2 and subtracted the result from equation 3. This gave:
4x - y + 3z = 6
and so finding the values of a and b was pretty simple from there. Plugging the numbers into a calculator gave an infinite number of solutions.
My question is, how can I better explain how to get a and b from the provided data? My method just seems like an educated guess rather than solid evidence - I don't think it'd look very good to an examiner. Cheers.
Homework Statement
Consider the following system of three equations in x, y and z.
2x + 4y + 5z = 17
4x + ay + 3z = b
8x + 7y + 13z = 40
Give values for a and b in the second equation that make this system consistent, but with an infinite set of solutions.
The Attempt at a Solution
I found the answers a= -1, b=6 easily enough. I was told by my teacher that if a system of three equations has infinite solutions, one of the equations can be found from the other two. I multiplied equation 1 by 2 and subtracted the result from equation 3. This gave:
4x - y + 3z = 6
and so finding the values of a and b was pretty simple from there. Plugging the numbers into a calculator gave an infinite number of solutions.
My question is, how can I better explain how to get a and b from the provided data? My method just seems like an educated guess rather than solid evidence - I don't think it'd look very good to an examiner. Cheers.
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