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09 Sep 2009, 06:17
Kudos
Bookmarks
I am hoping someone can clarify an issue that I am having with my study book for a basic math concept.
The book author states that:
"Often on the GMAT, you can solve a system of two equations in two unknowns by merely
adding or subtracting the equations—instead of solving for one of the variables and then
substituting it into the other equation."
For the example he provides, this approach (of course) works seamlessly as seen in Example #3:
However,...
In the very next explanation of the Method of Substitution, the example given does not seem to work if using the Adding/Subtracting of Equations method.
So, why is this so?...and if they do not compliment each other, then which am I supposed to know to use and/or what am I missing here?
Many thanks.
The book author states that:
"Often on the GMAT, you can solve a system of two equations in two unknowns by merely
adding or subtracting the equations—instead of solving for one of the variables and then
substituting it into the other equation."
For the example he provides, this approach (of course) works seamlessly as seen in Example #3:
However,...
In the very next explanation of the Method of Substitution, the example given does not seem to work if using the Adding/Subtracting of Equations method.
So, why is this so?...and if they do not compliment each other, then which am I supposed to know to use and/or what am I missing here?
Many thanks.
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09 Sep 2009, 06:52
Kudos
Bookmarks
The path to solving a system of equations is to eliminate all variables but one, find its value and then use it to calculate the other variables.
Method of substitution always works and it is simple and it guarantees that variables will be eliminated one by one but calculations can be too extensive. Sometimes it's better to use a short cut (add/subtract equations) to eliminate variables faster.
Here are a few examples:
1) Find x that satisfies the following system of equations:
135*x+233*y=1001
33*x-233*y = 15
If we blindly try to solve this equation using substitution method, that will work. From the first equation, x = (1001-233y)/135 -> second equation becomes: 33*(1001-233y)/135-233y=15 -> y can be found -> x can be calculated. A more elegant way would be to add equations, (135+33)x=1016 -> x = 1016/168 (done)
2) slightly different example with a trick (when substitution would take forever)
What is x, if (x,y,z,w) satisfy the following system of equations:
x+y+z=5
y+z+w = 7
z+w+x = 9
w+x+y = 12
Notice that we only need to find x. Also notice that if all equations are added, we get 3*(x+y+z+w)=5+7+9+12 -> x+y+z+w = 11 -> x = 11-7=4.
Method of substitution always works and it is simple and it guarantees that variables will be eliminated one by one but calculations can be too extensive. Sometimes it's better to use a short cut (add/subtract equations) to eliminate variables faster.
Here are a few examples:
1) Find x that satisfies the following system of equations:
135*x+233*y=1001
33*x-233*y = 15
If we blindly try to solve this equation using substitution method, that will work. From the first equation, x = (1001-233y)/135 -> second equation becomes: 33*(1001-233y)/135-233y=15 -> y can be found -> x can be calculated. A more elegant way would be to add equations, (135+33)x=1016 -> x = 1016/168 (done)
2) slightly different example with a trick (when substitution would take forever)
What is x, if (x,y,z,w) satisfy the following system of equations:
x+y+z=5
y+z+w = 7
z+w+x = 9
w+x+y = 12
Notice that we only need to find x. Also notice that if all equations are added, we get 3*(x+y+z+w)=5+7+9+12 -> x+y+z+w = 11 -> x = 11-7=4.
09 Sep 2009, 07:24
Kudos
Bookmarks
stilite
In the second example also, the method of adding / subtracting the equations works pretty fine. Just multiply the first equation by 2 (to get equal coefficient of y) , then add both the equations.
Using this method, y will get canceled out and you will get the value of x.
The same method is used in the first example which you have posted.
I hope it clarifies your doubt.
Note: Try to practice solving the questions by just adding / subtracting the equations. It will save you a lot of time which can eventually be used for some hard PS & DS problems.
) but I wanted to do a complete refresher course on my math from all that is tested on the GMAT.
