Math121 discussion - systems of equations

# Math121 discussion - systems of equations - SYSTEMS OF...

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SYSTEMS OF EQUATIONS WITH 2 VARIABLES (1) A system of equations is a collection of equations with the same set of variables. A system of linear equations will only have linear equations in it (i.e. equations of the form Ax + By + Cz + .... = 0 where x, y, z, etc. represent the variables and A, B, C, etc. represent the coefficients of the variables). (2) A solution to the system of equations will be the set of values that makes all the equations in the system true when you plug them in. In a 2-dimensional linear system, we call the solution an ordered pair ( x, y ), because the order matters (i.e. ( x, y ) 6 = ( y, x ) unless x = y ). (3) Graphically, the solution to a system of equations with 2 variables is the point(s) where the lines intersect on the xy-plane. If the lines do not intersect at any point, then there is no solution to the system. (4) A system of equations with 2 variables is generally of the form: ( Ax + By = C Dx + Ey = F (5) When we encounter a system with 2 variables, we should solve the system using elim- ination or substitution . in general, it is a better idea to use these methods than to

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