Question

How do you solve the following linear system: # 6x+y =3, 2x+3y=5 #?

Answer 1

`x=1/4, y=3/2`

Explanation:

In this case, we can use substitution, but I find using elimination simpler. We can see that if we do a little work, subtracting the two equations will let us solve for `y`.

`E_1: 6x+y=3`

`E_2: 2x+3y=5`

`E_2: 3(2x+3y)=3*5`

`E_2: 6x+9y=15`

`E_1-E_2: 6x+y-(6x+9y)=3-15`

`6x-6x+y-9y=-12`

`-8y=-12`

`y=(-12)/(-8)=3/2`

Now we plug in the solution to `y` into `E_1` to solve for `x`:

`E_1: 6x+3/2=3`

`6x=3-3/2`

`6x=3/2`

`x=(3/2)/6=3/12=1/4`