This means that both equations have the same solutions and thereby we can work with one or the other. And, by finding what the lines have in common, we’ll find the solution to the system. Then we can see all the points that are solutions to each equation. For a system of two equations, we will graph two lines. Each point on the line is a solution to the equation. The initial equation and the obtained oneĪre equivalent. The graph of a linear equation is a line. Let us not forget that if we multiply an equation by a number different from 0, Thus an equation with only one known factor is obtained.Įqualization: It consists in isolating fromīoth equations the same unknown factor to beĪble to equal both expressions, obtaining one equation with The equations, for example, adding or subtracting bothĮquations so one of the unknown factors disappears. Thus a first degree equation with the unknown factor y is obtained. Substitute that expression in the other equation. One of the unknown factors (for example x) and Substitution (elimination of variables): It consists in isolating In this section we will resolve linear systems of two equations and two unknown factors with the methods we describe next, which are based on obtaining a first degree equation (a linear equation). To solve consistent dependent a system, we need at least the same number of equations as unknown factors. We will not speak about other kinds of systems. If there is only one solution (one value for each unknown factor, like in the previous example), the system is said to be a consistent dependent system. There is not always a solution and even there could be an infinite number of solutions. For example,Ĭonsists in finding a value for each unknownįactor in a way that it applies to all the What these equations do is to relate all the unknown factors amongt themselves. A system of two linear equations is a set of two equations that need to be verified by the same solution. The theorem about solutions of homogeneous systems of equations. The unknown factors appear in various equations, but do not need to be in all of them. The theorem about solutions of systems of linear equations. 4 resolved systems of linear equations by substitution, addition and equalizationĪ system of linear equations (or linear system) is a group of (linear) equations that have more than one unknown factor.

Two equation systems