Question

Solve the system of linear equations below.

2x + y = 5
x + y = 4


I don't just want the answer can someone explain how to do this?

Answer 1

`x=1\\y=3`

Explanation:

You can use the Method of Elimination:

Multiply the first equation by -1, add both equations and then solve for the variable "x":

`\left \{ {{(-1)(2x + y )= 5(-1)} \atop {x + y = 4}} \right.\\\\\left \{ {{(-2x - y = -5} \atop {x + y = 4}} \right. \\.........................\\-x=-1\\\\(-1)(-x)=(-1)(-1)\\\\x=1`

Now substitute
`x=1` into any of the original equations and solve for the variable "y":

`x + y = 4\\1 + y = 4\\y=4-1\\y=3`