Question

How do you solve the system of equations `x= 6y - 7` and `x + 6y = 9`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for `x` we can substitute `(6y - 7)` for `x` in the second equation and solve for `y`:

`x + 6y = 9` becomes:

`(6y - 7) + 6y = 9`

`6y - 7 + 6y = 9`

`6y + 6y - 7 = 9`

`(6 + 6)y - 7 = 9`

`12y - 7 = 9`

`12y - 7 + color(red)(7) = 9 + color(red)(7)`

`12y - 0 = 16`

`12y = 16`

`(12y)/color(red)(12) = 16/color(red)(12)`

`y = 4/3`

Step 2) Substitute `4/3` for `y` in the first equation and calculate `x`:

`x = 6y - 7` becomes

`x = (6 xx 4/3) - 7`

`x = 24/3 - 7`

`x = 8 - 7`

`x = 1`

The Solution Is:

`x = 1` and `y = 4/3`

Or

`(1, 4/3)`

Answer 2

X=1, y= `8/6`

Explanation:

Rearrange equations to be in the form of x=...
Ie.
`x=9-6y`

Make these equations equal to each other
`6y-7=9-6y`

`16=12y`

`y=16/12` `=8/6`

Find x
#x=9-6(8/6) =9-8= 1#