Question #1553a

1 Answer
Jun 6, 2017

Answer:

Eliminating one variable allows you to solve for the other.

Explanation:

You cannot solve an equation that has #2# variables because there are infinitely many solutions.

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 #x# terms.

Case 2: If they have different signs, ADD the two equations:

Consider the equations below: the #x#-terms are additive inverses

#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 #y#-terms