| 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 an infinite number solutions. The simple reason is the 2 equations represent 2 lines that overlap each other. So they intersect each other at an infinite number of points. If we graph we can see that these two lines are the same. So this system is dependent |
| 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 2 and 3 to some equal number, we could try to get them to the LCM. Since the LCM of 2 and 3 is 6, we need to multiply both sides of the top equation by 3 and multiply both sides of the bottom equation by -2 like this: So after multiplying we get this: Notice how 6 and -6 add to zero (ie Now add the equations together. In order to add 2 equations, group like terms and combine them So after adding and canceling out the x terms we're left with: Now plug this answer into the top equation So our answer is which also looks like ( Notice if we graph the equations (if you need help with graphing, check out this solver) we get and we can see that the two equations intersect at ( |
| 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 when we multiply Now that we know that So this is the other answer So our solution is which can also look like ( Notice if we graph the equations (if you need help with graphing, check out this solver) we get and we can see that the two equations intersect at ( ----------------------------------------------------------------------------------------------- Check: Plug in ( Let So the solution ( Let So the solution ( Since the solution ( this verifies our answer. |