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Definition

coefficient

1) In a mathematical equation, a coefficient is a constant by which a variable is multiplied. Consider the following equations:

3 x 2 + 5 x - 3 = 0
ax 3 + by 2 = z

The values 3 and 5 in the first equation are coefficients of x , a variable. In the second equation, if a and b are constants, then a is a coefficient of x 3 , and b is a coefficient of y 2 . It is customary to use lower-case, italic letters from the first half of the alphabet to represent constants whose values are not specified numerically. Lower-case, italic letters from the second half of the alphabet generally represent variables.

2) In physics and engineering, a coefficient is a quantitative expression of a specific property of matter, or of a phenomenon. Consider an electronic component whose value changes with temperature. It is tested and found to have a resistance of 100 ohm s at a temperature of +20 degrees Celsius (°C), and a resistance of 101 ohms at a temperature of +70 °C. This is the equivalent of a change in resistance of +1 ohm for a temperature change of +50 °C, or +0.02 ohm per degree Celsius. Between temperatures of +20 °C and +70 °C, therefore, this component has a temperature coefficient of +0.02 ohm per degree Celsius, assuming the resistance-versus-temperature function is linear over that range of temperatures.

This was last updated in September 2005

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Is x = 3 and y = -10 a solution of the equation -7x + 6y = 15?
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x = -2.1428571428571428571428571428571
y = 2.5
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you carry the number to the other side of the equal sign and reverse its operation.
So, x = 15 divide 15 by -7 and that 'x' becomes -2.142857142857...
Repeat this process, y = 15 divided by 6 and  'y' becomes 2.5
You can check this by simple doing the math
(-7 x -2.1428571428571428571428571428571) + (6 x 2.5) = 30 which is twice the number you are looking for, so since there are 2 variables you divide -2.1428571428571428571428571428571(x) by 2 = -1.0714285714285714285714285714286 
Now, divide 2.5 (y) by 2 = 1.25
Thus, giving you the full equation of
(-7 x -1.0714285714285714285714285714286 ) + (6 x 1.25) = 15
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((-7) x (-1.0714285714285714285714285714286)) + (6 x 1.25) = 15

Is the proper representation of the equation, but any way, I hope this helps.
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((-7) x (-1.0714285714285714285714285714286)) + (6 x 1.25) = 15

Is the proper representation of the equation, but any way, I hope this helps you to not only know why this is the answer, but how it came to be.
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Don't listen to ElConquistador  he has no idea what he's talking about.
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