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# A Definition of Algebra

Algebra is a mathematical system It involves letters numbers symbols and a variety of equations Equations are systems of inequality between two expressions There are many types of equations In the paragraphs below I will introduce to you three different systems of equations and how to solve them One way to solve an equation is to graph There are three different steps in graphing equations to solve The first thing you want to do is put the given equation into slope-intercept form y mx b For example if you are given the equation x y 6 to put that into slope-intercept form you must subtract the x from both sides Therefore you would end up with y -x 6 which can be graphed Another important fact in graphing is finding the slope of a line To find the slope of a line you should use the equation m This can be used if you are given two sets of points Another equation used is y - y1 mx-x1 This is helpful in finding the slope of a line Second I will talk about the substitution method Substitution is another important way to solve a system of equations In substitution there are three steps First you must solve for one variable in one out of the two given equations For example If you are given x y 6 and x - y 24 You are now able to substitute for x in the first equation - y 24 y 6 Now all that is left to do is solve for y in which you would get y 9 After you have solved for y you can go back and solve for x by substituting y into the first equation x - 9 6 Now all that is left to do is solve the equation

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