Question

Question #1553a

Answer 1

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