Question

How do you solve systems of linear equations by graphing `4x+y=13` and `2x-y=5`? {x+y=20 { x=3y 2x+4y=6 5x+10y=15?

Answer 1

See below:

Explanation:

I think I'm seeing 3 different systems of equations:

`System 1: 4x+y=13; 2x-y=5`
`System 2: x+y=20; x=3y`
`System 3: 2x+4y=6; 5x+10y=15`

System 1: 4x+y=13; 2x-y=5

graph{(4x+y-13)(2x-y-5)=0}

`(x,y)=(3,1)`

System 2: x+y=20; x=3y

graph{(x+y-20)(x-3y)=0[10,20,0,10]}

`(x,y)=(15,5)`

System 3: 2x+4y=6; 5x+10y=15

graph{(2x+4y-6)(5x+10y-15)=0}

In this case, the two graphs are identical (they both reduce to `y=-1/2x+3/2`) and so the solution set is all points along the line.