Question

How do you solve the following system: `7y − 6x − 5 = 0, -5x − y = 14`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the second equation for `y`:

`-5x - y = 14`

`-5x - color(blue)(14) - y + color(red)(y) = 14 - color(blue)(14) + color(red)(y)`

`-5x - 14 - 0 = 0 + y`

`-5x - 14 = y`

`y = -5x - 14`

Step 2) Substitute `(-5x - 14)` for `y` in the first equation and solve for `x`:

`7y - 6x - 5 = 0` becomes:

`7(-5x - 14) - 6x - 5 = 0`

`-(7 xx 5x) - (7 xx 14) - 6x - 5 = 0`

`-35x - 98 - 6x - 5 = 0`

`-35x - 6x - 98 - 5 = 0`

`(-35 - 6)x - 103 = 0`

`-41x - 103 = 0`

`-41x - 103 + color(red)(103) = 0 + color(red)(103)`

`-41x - 0 = 103`

`-41x = 103`

`(-41x)/color(red)(-41) = 103/color(red)(-41)`

`(-color(red)(cancel(color(black)(41)))x)/cancel(color(red)(-41)) = -103/41`

`x = -103/41`

Step 3) Substitute `-103/41` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = -5x - 14` becomes:

`y = (-5 xx -103/41) - 14`

`y = 515/41 - (41/41 xx 14)`

`y = 515/41 - 574/41`

`y = -59/41`

The Solution Is:

`x = -103/41` and `y = -59/41`

Or

`(-103/41, -59/41)`