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in order to balance equations, coefficients are placed in front of the various compounds/elements. This is done so that the same number of atoms are produced on each side of the equation.
For example: *2*H20 = *2*H2 + 02
The numbers with asterisks on either side of them are coefficients. Without them, there would be only one hydrogen atom on the products side and two on the reactants side. In order to preserve the law of conservation of mass, you must add a coefficient of two. So, you multiply the coefficient by the however many atoms there are.
Then, the equation is balanced and your teacher is happy.
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Solve linear equations with complex coefficients on both sides?
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
How does the method for solving equations with fractional or decimal coefficients and constants compare with the method for solving equations with integer coefficients and constants?
The method is the same.
What are the common characteristic between simultaneous linear equations in 2 unknowns which have no solutions?
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
Why are coefficients used in chemical equations?
to determine the mole of the atom
What makes a system of equations dependent?
If one (or more) of the equations can be expressed as a linear combination of the others. This is equivalent to the statements the matrix of coefficients does not have an inverse (or is singular), or the determinant of the matrix of coefficients is zero.
