Saturday, August 22, 2009
Solving Systems of Equations
We have been learning about solving systems of equations. When solving systems, the goal is to find out what value for the variables will satisfy both equations. We have learned the various methods to accomplish this. First, you can graph the two equations to find their solution. Second, you can isolate one variable and use substitution. Lastly, you can use the elimination method by subtracting the two equations. Pick one method to describe and provide an example of a system when you would use it.
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The substitution method can be used when it is easy to isolate a variable in one equation. For example, if one of the equations was x +6 = 4y, you could isolate x by subtracting 6 from both sides. Then your new equation would be x = 4y - 6. Next, you would substitute this new value for x into the second equation. If the second equation was 5x + 3 = 2y, you would replace x and get 4y - 6 + 3 = 2y. Since you would only have y in your new equation, you can easily solve for y! After solving for y, you would plug the value for y into one of the equations and find x. Substitution is the best option when you can easily isolate a variable.
ReplyDeleteThe elimination method is the best choice when you have two equations that have the same coefficient in front of either the y or x value. For example, if your two equations were 4x+6 = 3y and 4x -8 = 5y, you can subtract these two equations and you would only be left with the constant and y term. This would happen because the x terms cancel each other out. You line the two equations up and subtract like terms on each side of the equal sign. After you have eliminated the x term, you would simplify the new equation to solve for y. After finding the y term, you plug the new value into one of the original equations and find the value of x!
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