Question

How do you solve the system of equations `4x - 8y = 15` and `- 5x + 10y = - 30`?

Answer 1

See a solution process below:

Explanation:

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

`-5x + 10y = -30`

`-5x + 10y - color(red)(10y) = -30 - color(red)(10y)`

`-5x + 0 = -30 - 10y`

`-5x = -30 - 10y`

`(-5x)/color(red)(-5) = (-30 - 10y)/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5)) = (-30)/color(red)(-5) - (10y)/color(red)(-5)`

`x = 6 + 2y`

Step 2) Substitute `(6 + 2y)` for `x` in the first equation and solve for `y`:

`4x - 8y = 15` becomes:

`4(6 + 2y) - 8y = 15`

`(4 * 6) + (4 * 2y - 8y = 15`

`24 + 8y - 8y = 15`

`24 + 0 = 15`

`24 != 15`

There is no solution to this system of equations. Or, the solution is the null or empty set: `{O/}`

This indicates the lines are parallel lines but are not the same line.