Question

How do you solve the system 5x - y = 3 and -10x + 2y = -6?

Answer 1

See a solution process below:

Explanation:

Both of these equations are almost in the Standard Form for linear equations. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

We can get the second equation closer to Standard Form by multiplying both sides of the equation by `-1`:

`-1(-10x + 2y) = -1 * -6`

`10x - 2y = 6`

Now, we can divide each side of the equation by `2` to get this equation into true standard form:

`(10x - 2y)/2 = 6/2`

`5x - y = 3`

These equations are actually the same equation. Therefore, the solution to this is they have all points in common.