Question

How do you solve the system of equations `10x = - 2y + 1` and `0= 5x + y - 9`?

Answer 1

See a solution process below:

Explanation:

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

`0 - color(red)(5x) + color(blue)(9) = 5x - color(red)(5x) + y - 9 + color(blue)(9)`

`-5x + 9 = 0 + y - 0`

`-5x + 9 = y`

`y = -5x + 9`

Step 2) Substitute `(-5x + 9)` for `y` in the first equation and solve for `x`:

`10x = -2y + 1` becomes:

`10x = -2(-5x + 9) + 1`

`10x = (-2 xx -5x) + (-2 xx 9) + 1`

`10x = 10x + (-18) + 1`

`10x = 10x - 18 + 1`

`10x = 10x - 17`

`10x - color(red)(10x) = 10x - color(red)(10x) - 17`

`0 = 0 - 17`

`0 != -17`

Because we know `0` does not equal `-17` it means there is no solution to this problem.

Or, the solution is the empty or null set: `x = {O/}`

This also indicates the two lines represented by the equation in the problem are parallel lines and not the same lines.