Question

How do you solve the system of equations `13x - 5y = 20` and `13x - 5y = 10`?

Answer 1

The system has no solution because its equations are incompatible.

Explanation:

Solve a system like this:

`13 x - 5 y = 20`
`13 x - 5 y = 10`

means we have to find values `x` and `y` that makes true both equations at same time.

In that system we have here, if we try to solve it, for example, using reduction method, we obtain something like that:

`color(white) "....." 13 x - 5 y = 20`
`- (13 x - 5 y = 10)`
`"—————————"`
`color(white) "................." 0 = 10`

i.e. a false identity. This means that no exists any value for `x` and `y` that match both equations at same time, i.e. system is incompatible.