Eliminating one variable allows you to solve for the other.
You cannot solve an equation that has
As soon as you have 2 equations, there is a specific solution.
However, you need to get rid of one of the variables temporarily so that you can find a value for the one that is left.
This is done by making sure that the variable that is to be eliminated has the same numerical coefficients.
Case 1: If they have the SAME sign, subtract the two equations:
Consider the equations below:
#5xcolor(blue)(+5y) = 30#
#3x color(blue)(+5y) =22#
Subtracting the two equations will lead to
#2x color(blue)(+0y) = 8" "larr#the #y#-terms have been eliminated
The difference between the two equations represents the difference in just the
Case 2: If they have different signs, ADD the two equations:
Consider the equations below: the
#color(red)(+4x)+3y = 29#
#color(red)(-4x) +5y =-5#
Adding the two equations leads to:
#color(red)(0x)+8y=24" "larr#the #x#-terms have been eliminated
The sum of the equations gives us the sum of just the