stapel_eliz wrote:I've never heard of the "comparison" method. How does that work? Can you give an example from your book, or maybe a link? (All I could find is
a PDF worksheet that makes it look like "comparison" is just a form of "substitution", where both equations are already solved for one of the variables.)
Thank you!
This is the text from my book:
"Another way to eliminate a variable from a system is sometimes referred to as the comparison method. Solve for the same variable in each equation; then form one equation by setting those two expressions equal to each other. The idea is that if two quantities are equal to the same thing, then they must equal each other.
We will solve the same system that we just did but use this method so that you can compare the two solutions. Both are correct solutions; the different method just gives you more options when you wish to solve a system algebraically.
Example:
Solve the following system of equations by the comparison method.
2x + 6y + 3 = 0
x - 4y - 9 = 0
Solution:
Make y the subject of each equation; then solve each equation:
2x + 6y + 3 = 0
6y = -2y - 3
x - 4y - 9 = 0
-4y = -x + 9
Combine the two results into a single equation of the results and find the value of x:
Substitute 3 in for x into one of the original equations and solve for y:
2(3) + 6y + 3 = 0
6 + 6y + 3 = 0
6y + 9 = 0
6y = -9
y = -
The checks were shown above."
Can you explain that in simpler terms?