Question

How do you solve `y+6=2x` & `4x-10y=4`?

Answer 1

`x=7/2` and `y=1`

Explanation:

Strategy: Solve for `y` in terms of `x`. Plug in that `y` equation into the other equation to solve for `x`. With the solution for `x`, you can back track and find the solution for `y`.

Step 1. Solve for `y` in terms of `x`.
`y+6=2x` given
`y=2x-6` subtract 6 from both sides

Step 2. Plug this `y` equation into the other equation.
`4x-10color(red)(y)=4` ; given
`4x-10(color(red)(2x-6))=4` ; replace variable `y` with `2x-6`
`4x-20x+60=4` ; distribute `-10` through
`-16x=-56` ; combine `x` terms and subtract `60` both sides
`x=7/2` ; divide both sides by `-16 and reduce`

Step 3. Plug this solution back into the equation of step 1.
`y=2color(red)(x)-6` ; final part of step 1
`y=2(color(red)(7/2))-6` ; solution for `x` in step 2
`y=7-6=1`

So your solution is `x=7/2` and `y=1`

Answer 2

`(7/2,1)`

Explanation:

`color(red)(y)+6=2xto(1)`

`4x-10color(red)(y)=4to(2)`

`"note that in " (1)" y can be expressed in terms of x"`

`rArrcolor(red)(y)=2x-6to(3)`

`"substitute into " (2)`

`rArr4x-10(2x-6)=4`

`rArr4x-20x+60=4larr" distributing"`

`rArr-16x+60=4larr" simplifying left side"`

`"subtract 60 from both sides"`

`-16xcancel(+60)cancel(-60)=4-60`

`rArr-16x=-56`

`"divide both sides by - 16"`

`(cancel(-16) x)/cancel(-16)=(-56)/(-16)`

`rArrx=56/16=7/2`

`"substitute this value in " (3)" and evaluate for y"`

`y=(2xx7/2)-6=7-6=1`

`(7/2,1)" is the point of intersection of the 2 equations"`
graph{(y-2x+6)(y-2/5x+2/5)=0 [-10, 10, -5, 5]}