Question

How do you solve the system of equations `8x=2y+5` and `3x=y+7` using substitution?

Answer 1

Find an expression for `y` and work from there to get a solution of `(-9/2,-41/2)`.

Explanation:

I'll start by labeling each equation to make the solving process easier to follow:
`i.............8x=2y+5`
`ii............3x=y+7`

Start by subtracting `7` from both sides of equation `ii:`
`3x=y+7`
`3x-7=y+cancel(7)-cancel(7)`
`->y=3x-7`

Now substitute this into equation `i` for `y`:
`8x=2y+5`
`8x=2(3x-7)+5`

And solve for `x`:
`8x=2(3x-7)+5`
`8x=6x-14+5`
`2x=-9`
`x=-9/2`

We found earlier that `y=3x-7`. We now have the value of `x`, so we'll use it to find `y`:
`y=3x-7`
`y=3(-9/2)-7`
`y=-27/2-7`
`y=-27/2-14/2`
`y=-41/2`

The solution, then, is `(-9/2,-41/2)`.