Question

Solve this system of equations? `3x+y=8 and 4x+2y=9`

Answer 1

`(x,y)=(7/2,-5/2)`

Explanation:

Let's use substitution. We can solve the first equation for `y` then substitute that into the second equation:

`E1: 3x+y=8 => y=8-3x`
`E2: 4x+2y=9 => 4x + 2(8-3x)=9`

So now let's solve `E2` for `x`:

`4x + 2(8-3x)=9`

`4x+16-6x=9`

`-2x=-7`

`color(blue)(ul(bar(abs(color(black)(x=7/2`

And now let's substitute this `x` value back into one of the original equations (I'll use the `E1` where we solved for `y`):

`y=8-3x`

`y=8-3(7/2)`

`color(blue)(abs(ul(bar(color(black)(y=16/2-21/2=-5/2`

Here's the graph:

graph{(3x+y-8)(4x+2y-9)=0[2.5,5,-5,0]}