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lustrog
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why does adding equations solve the system of equations? I've taken matrix algebra but, to be honest, was too bashful to ask such a simple question. :P
Because they are the same value! That's exactly what the "simultaneous" in "simultaneous equations" means- find specific values of x, y, etc. that satisfy all of the equations.lustrog said:much appreciated, mark44. one of the things that bothered me is why you can treat the x's and y's of each equation as the same value. but your response put me on the right track to clearing that up too, because if you think about it in two steps it makes sense.
(if anyone else has been bothered by this also, here is the way I'm thinking about it now):
if you take y's equal at any given point, but let the x's from each equation, x_1, and x_2 be anything, then you can add the two equations together to find that when y's are equal, you have x_1 + x_2 = 4. but we're interested when it is also the case that x_1 = x_2, so we have that 2*x = 4 and x = 2.
i don't know why i sometimes get hung up on such things when others don't but this was very helpful. thanks again.
lustrog said:why does adding equations solve the system of equations? I've taken matrix algebra but, to be honest, was too bashful to ask such a simple question. :P
A system of equations is a set of two or more equations with multiple variables that are meant to be solved simultaneously. The solution to a system of equations is the set of values for each variable that satisfies all of the equations in the system.
The most common method for solving a system of equations is by using the substitution or elimination method. In the substitution method, one equation is solved for a variable and then substituted into the other equation. In the elimination method, the equations are manipulated to eliminate one variable and solve for the remaining variable.
Yes, a system of equations can have any number of variables. However, the number of equations in the system must be equal to the number of variables in order for there to be a unique solution.
A consistent system of equations has at least one solution that satisfies all of the equations in the system. An inconsistent system of equations has no solution, meaning there is no set of values that satisfies all of the equations.
You can check your solution by plugging the values of the variables into each equation in the system. If the solution is correct, the resulting values should satisfy all of the equations in the system and produce a true statement for each equation.