Question

How do you solve the system of equations `-7x - y = - 11` and `6x + 7y = - 9`?

Answer 1

x=2, and y=-3 form the solution.

Explanation:

The equations are solved by the method of elimination and substitution.
Given:
`-7x-y=-11--------(1)`
`6x+7y=-9---------(2)`
Eliminate y from 1 and 2
Multiplying (1) by 7
`-49x-7y=-77--------(3)`
Adding (2) and (3)
`-43x=-86`
Dividing by 43,
`x=2`
Substituting for x in (1)
`(-7) (2)-y=-11`
`-14-y=-11`
Rearranging
`-14+11=y`
`y=-3`
Check:
(1)---`lhs =(-7)(2)-(-3)=-14+3=-11=rhs`
and
(2(---`lhs=(6)(2)+(7)(-3)=12-21=-9=rhs`

Answer 2

See a solution process below:

Explanation:

Step 1) Solve each equation for `7y`:

• Equation 1: `-7x - y = -11`

`-7x + color(red)(7x) - y = -11 + color(red)(7x)`

`0 - y = -11 + 7x`

`-y = -11 + 7x`

`color(red)(-7) xx -y = color(red)(-7)(-11 + 7x)`

`7y = (color(red)(-7) xx -11) + (color(red)(-7) xx 7x)`

`7y = 77 - 49x`

• Equation 2: `6x + 7y = -9`

`6x - color(red)(6x) + 7y = -9 - color(red)(6x)`

`0 + 7y = -9 - 6x`

`7y = -9 - 6x`

Step 2) Because the left side of both equations are equal we can equate the right side of both equations and solve for `x`:

`77 - 49x = -9 - 6x`

`77 + color(blue)(9) - 49x + color(red)(49x) = -9 + color(blue)(9) - 6x + color(red)(49x)`

`86 - 0 = 0 + (-6 + color(red)(49))x`

`86 = 0 + 43x`

`86 = 43x`

`86/color(red)(43) = (43x)/color(red)(43)`

`2 = (color(red)(cancel(color(black)(43)))x)/cancel(color(red)(43))`

`2 = x`

`x = 2`

Step 3) Substitute `2` for `x` in either of the equations in Step 1 and solve for `y`:

`7y = -9 - 6x` becomes:

`7y = -9 - (6 xx 2)`

`7y = -9 - 12`

`7y = -21`

`(7y)/color(red)(7) = -21/color(red)(7)`

`(color(red)(cancel(color(black)(7)))y)/cancel(color(red)(7)) = -3`

`y = -3`

The Solution Is:

`x = 2` and `y = -3`

Or

`(2, -3)`