How do you know what number to multiply everything by using the elimination method on systems of equations? ?

See below  

Step-by-step explanation:

You multiply the equations by numbers that will give you the least common multiple of the coefficients.

Suppose you have a system of two equations:

You can choose to eliminate either x or y.

1. Eliminating x

The coefficients of x are 2 and 1. The least common multiple is 2, so you multiply (1) by 1 and (2) by 2 to get

Then you can subtract (3) from (4) and get

4y = 80. Solve for y.

2. Eliminating y

The coefficients of y are 1 and 2.5. The least common multiple is 2.5, so you multiply (1) by 2.5 and (2) by 1 to get

Then you can subtract (6) from (5) and get

4x = 40. Solve for x.