Multiply the first equation by 1/2 and add it to the second equation to obtain the system
Since the second equation obviously has no solution, this system, and hence the original system, is inconsistent. Thus the solution set of the original system isĪdd -2 times the first equation to the second equation to obtain the system The method of solution by elimination depends on the elementary operations E1, E2, and E3 below, which change a given system into an equivalent system.Į.1 Interchange any two equations of the system.Į.2 Multiply any equation by a nonzero number.Į.3 Replace any equation of the system by the sum of that equation and a multiple of another equation of the system.Īpplying E.3 we multiply the first equation by -2 and add it to the second equation obtaining the systemĪpply E.2 to the second equation by multiplying by -1/5. Click on 'Solve Similar' button to see more examples. Let’s see how our math solver solves this and similar problems. The original system is therefore inconsistent. We write A, the solution set of the system is If A and Bare sets, then we say that A is a subset of B if each element of A is also an element of B. In order to better understand the concept of solving a system of equations, we will need to become familiar with some facts on sets.