Question

How do you solve the following system: #2x+7y=1, 6x + 7y = -9 #?

Answer 1

By arranging it, it can be calculated that `x=-5/2` and `y=6/7`

Explanation:

The first equation can be rewritten
`-6x - 21y = -3` (after multiplication by -3)
`6x + 7y = -9` (the second original equation)

Combine these two equations:
`-14y = -12`

`y=12/14`
or
`y=6/7`

Now put value in the first original equation:

`2x = 1 - (7times(6/7))`

`2x = 1-6`

`x=-5/2`

The answer is `x=-5/2` and `y=6/7`

Answer 2

`x= -2.5 and y= 6/7`

Explanation:

Note that the number of `y`s in both equations stays the same.
The difference in the the totals therefore represents the difference in the number of `x`s. Subtract the two equations:

`" "6xcolor(blue)(+7y) =-9" ".........A`
`" "ul(2xcolor(blue)(+7y) =+1)" ".........B`

`A-B" "4x = -10" "`solve for `x`

`" "x = -2.5`

Substitute `-2.5` for `x` to find `y` in B

`2(-2.5) +7y =1`

`" "-5 +7y = 1`
`" "7y =1+5`
`" "7y =6`
`" "y = 6/7`

Check in A:
`6xx(-2.5)+7(6/7)`

`=-15+6 =-9`
This is correct.