Question

What is the solution to the following system of equations? x+y=5

x-y=1

Answer 1

(3,2)

Explanation:

Let's solve this via elimination method:

`\begin{cases} x+y=5\\x-y=1\end{cases}`

By subtracting equation 2 from equation one we obtain:

`\begin{cases} x+y=5\\-(x-y=1)\end{cases}\\\\0x+2y=4\\\\y=2`

Next we can use any equation either 1 or 2 to determine what x is, I'll use equation 1. Let y=2 and so:

`x+y=5\\\\x+2=5\\x=5-2\\\\x=3`

Therefore the solution for the system of equations is:

x=3 and y = 2 as an ordered pair we have (3,2)