Question

Graph the system of equations on your graph paper to answer the question. {y=−x+4y=x−2 What is the solution for the system of equations?

Answer 1

`\left\{\begin{array}{ccc}y=-x+4&(1)\\y=x-2&(2)\end{array}\right\\\\(1)\\for\ x=0\to y=-0+4=4\to(0;\ 4)\\for\ x=4\to y=-4+4=0\to(4;\ 0)\\(2)\\for\ x=0\to y=0-2=-2\to(0;\ -2)\\for\ x=2\to y=2-2=0\to(2;\ 0)\\\\\text{the graph in attachment}\\\\\text{Answer:\ x=3;\ y=1}`

Answer 2

The solution for the system of equations is
`x=3, y=1`

Explanation:

we have

`y=-x+4` -----> equation A

`y=x-2` -----> equation B

we know that

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The intersection point is
`(3,1)`

see the attached figure

therefore

The solution for the system of equations is

`x=3, y=1`