# Graphing, substitution, linear combination

Essay by suchy23High School, 10th gradeA, December 2004

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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 = m(x-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...