# 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?

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}

$\left(x , y\right) = \left(3 , 1\right)$

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

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

$\left(x , y\right) = \left(15 , 5\right)$

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 $y = - \frac{1}{2} x + \frac{3}{2}$) and so the solution set is all points along the line.