Elimination or Substitution? How to Choose the Faster Method

Both elimination and substitution solve simultaneous equations, but one method is often noticeably shorter for a particular pair.

Use substitution when a variable is already isolated

For example:

The first equation already tells you what y equals, so substitute 2x + 1 into the second equation.

Use elimination when coefficients already match

For:

The y coefficients are both +3. Subtracting the equations removes y immediately.

Look for an easy multiple

If the coefficients do not match but one is a simple multiple of the other, elimination may still be quickest. For example, coefficients 2 and 4 are easy to align.

Do you have to use the shortest method?

No. A correct method is still correct. Choosing the shorter route simply reduces the amount of arithmetic and therefore the number of places where mistakes can happen.