Elimination for Equations

 

Sometimes when answering a question on the SAT math section it is necessary to use elimination to get the final answer. To do this, it is simply a matter of lining up two equations and adding or subtracting them to get rid of one of the variables. At that point, it is necessary to substitute the information into one of the equations to get the answer for the second variable, which is the final answer of the question.  As with other sections of the SAT math portion, questions surrounding elimination are written to be intentionally tricky and confusing for test takers. Because of this, it is important to read the questions carefully and follow them to the letter in order to get the correct answer and a higher overall SAT math score.  Elimination Example 2x + 5z = 18 and 10x - 5z = 30, what is z? First, line up the equations like they were regular numbers.  2x + 5z = 12 + 10x - 5z = 28 After this, add each column.  2x + 5z = 18 + 10x - 5z = 30 12x + 0z = 48 At this point, one variable should be eliminated by getting it to 0 (zero). At this point, it is possible to solve for X.   12x = 48 x = 4 Now that X is known, it should be substituted into one of the other two equations to solve it for the other one.  2x + 5z = 18 2•4 + 5z = 18 8 + 5z = 18 5z = 10 z = 2 So z = 2 and x = 4. TIP: Sometimes, it will be necessary to multiply one or both equations all the way through by using an integer. This is done to create numbers that will eliminate nicely in the equation.