Answer:
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:
[tex]\begin{cases}(1)& 2x + y = 40\\(2) & x + 2.5y = 60\end{cases}\\[/tex]
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
[tex]\begin{array}{lrcll}(3) & 2x + y & = & 40 &\ \\(4) & 2x + 5y & = & 120 & }\\\end{array}[/tex]
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
[tex]\begin{array}{lrcll}(5) & 5x + 2.5y & = & 100 &\ \\(6) & x + 2.5y & = & 60 & }\\\end{array}[/tex]
Then you can subtract (6) from (5) and get
4x = 40. Solve for x.
