| Solved by pluggable solver: Solving a linear system of equations by subsitution |
Lets start with the given system of linear equations Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y. Solve for y for the first equation Which breaks down and reduces to Since y equals So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist. and we can see that the two equations are parallel and will never intersect. So this system is inconsistent |
| Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition |
Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero. So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 3 and 3 to some equal number, we could try to get them to the LCM. Since the LCM of 3 and 3 is 3, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -1 like this: So after multiplying we get this: Notice how 3 and -3 and 1 and 1 add to zero (ie However 1 and -2 add to -1 (ie So we're left with which means no value of x or y value will satisfy the system of equations. So there are no solutions So this system is inconsistent |