This is a free lesson from our course in Algebra I This lesson introduces systems of linear equations and explains related concepts. A system of equations is a set of equations in one or more variables, and its solution is a set of values for its variables such that when these values are substituted into the equations, the equations are 'satisfied' i.e. the results are equalities. For example,  x + y + z =0 and x - y - 4z= 0 is a system of two equations in the three variables . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by x = 1 , y = 2 , z = -3 since it makes both equations valid. (More text below video...)
Other useful lessons:
 Finding intersection points graphically Determine if a systems of equations has no solution Determine if a system of equations has infinite solutions
(Continued from above) If this seems too complicated, it really isn't -- when you hear the instructor explain it to you in the video above, you'll see how easy it is. Sometimes, text based explanations of mathematical concepts seem complicated, but when you actually hear from someone what they mean, they are not that difficult to understand! You'll also look at inequalities here -- an inequality, unlike an equation, does not use the = symbol, but instead uses one of these symbols: <, >, <=, >=. For example, 2x + 3y <= 5. In this inequality, whatever you plug in for values of x and y, the expression is only valid if the value of 2x + 3y is less than 5 or equal to 5.
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