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.
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.
The method is the same.
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
When the coefficients of either variable are different in a system of equations, you can use methods such as substitution or elimination to solve for the variables. If using elimination, you may need to multiply one or both equations by a factor to make the coefficients of one variable the same, allowing you to add or subtract the equations effectively. For substitution, isolate one variable in one equation and substitute it into the other. This will help you find the values of the variables.
to determine the mole of the atom
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.
The method is the same.
coefficients
parameters
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
to determine the mole of the atom
When the matrix of coefficients is singular.
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.
Both. you must have the correct subscripts to represent the correct chemical then you only change the coefficients to balance the equation. The product of a coefficient and a subscript tells how many atoms are present.
Coefficients
It is necessary to know the reactants, the products and the valences.