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There are several methods to do this; the basic idea is to reduce, for example, a system of three equations with three variables, to two equations with two variables. Then repeat, until you have only one equation with one variable.
Assuming only two variables, for simplicity:
One method is to solve one of the equations for one of the variables, then replace in the other equation.
Another is to multiply one of the equations by some constant, the other equation by another constant, then adding the resulting equations together. The constants are chosen so that one of the variables disappear.
Specifically for linear equations, there are various advanced methods based on matrixes and determinants.
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What can systems of equations be solved by?
By elimination or substitution
What is a systems of equations that has the same solution set as another system?
They are called equivalent systems.
When are systems of linear equations used?
In coordinated geometry on the Cartesian plane
Can systems of equations with the same slopes and different y-intercepts have no solution?
It is a correct statement.
How can systems of equations be solved?
It depends on your level of expertise. The simplest method is to invert the matrix of coefficients.
