Simultaneous Equations

Similar to elimination problems - which is used to trick students - simultaneous equations are not solved by solving a single variable first. Instead, a simultaneous equation needs to be solved all at once - the entire expression. The difference between the two is slight, but understanding and being able to recognize the differences is important so that test takers can get the final answer correct and get a higher overall SAT math score.  Simultaneous Equations The key to solving simultaneous equations is to decide whether addition or subtraction will be needed. It is important to note that when subtracting the negative must be distributed throughout the entire equation. This is a simple mistake that can cause a person to get the wrong answer, which will usually be one of the choices available in the multiple choice section. Like elimination problems, simultaneous equations should be multiplied all the way through to get the correct answer at the end.  TIP: There may not be a reason to multiply the equation through with anything other than a simple number like 2,3 or -3. Experimenting by putting one equation on top and then the other, it should be really easy to see which way it is supposed to go as well as getting the final correct answer, which is important for the overall SAT math score.  Simultaneous Equations Tip TIP: When not sure to use elimination, substitution or simultaneous equations to solve a problem on the math section of the SAT, it is crucial to examine the question carefully to see what the test makers are looking for as the answer. When they ask for more than one variable, it is usually easier to solve for that expression rather than figure out what each variable would be separately. This can save time and allow for more questions to be answered, which can dramaticaly increase the SAT math score.  Simultaneous Equation Word Problems For word problems, it is simply a matter of using a variable for unknowns in the question. For example.  Terry is 3 years younger than twice Heather's age. If Heather will be 15 in two years, how old is Terry? The unknown variables in this question are Terry and Heather's age. It is possible to use the variable T and H instead of X and Y to make it easier to remember which is which when solving the problem.  t = x - 2h - 3 If Heather's age is currently H then her age in two years would be H + 2, which means 2 + h = 15. This would make her age 13, which can be used to solve the rest of the equation. As you can see, the real trick is in reading the word problem and being able to translate it into a math equation. This is the part that most people have problems with when doing Simultaneous Equation word problems.  Another Simultaneous Equation Word Problem  If Heidi is 19 months older than her cousin Tim and four years older than her other cousin Kate and the sum of her cousin's age is 20 years old, how old is Heidi? In this question, the problem is to choose which name to use as a variable. While any would work, it is best to use Heidi since that is what the final answer wants. Because 19 months is not a whole year, decimals will need to be used. For example, this case would be 19 / 12 which would be 1.583 years. Now that this information is known, the rest of the answer is simply a matter of using algebra to come up with the final answer.