Solve using the elimination method

y = all real numbers

x = all real numbers

In set notation/interval notation;

y∈(-∞,∞)

x∈(-∞,∞)

Step-by-step explanation:

1. Background information

The process of elimination involves manipulating an equation such that when the equations in the system are added, one variable is eliminated. Then one can solve for the other variable, finally, one substitutes the answer back in to find the eliminated variable. Therefore solving the system of equations.

2. The given information

Given the system;

(1)    4x + 5y = 4

(2)    8x + 10y = 8

3. Solving

Multiply the first equation by (-2)

4x + 5x = 4

*-2           *-2

-8x - 10x = -8

Add the first and second equations.

   -8x - 10y = -8

+ ( 8x + 10y = 8 )

0

This means that y can be any real number, and hence x can be any real number.

x = 3 ± √(5+y)