# How do you solve the following system of equations #x - 2y = 5# and #2x - 4y = 10#?

##### 2 Answers

Since

They are really the same equation with an infinite number of solutions

.

Any pair

We could use substitution or the addition/subtraction method.

Let's use substitution:

We'll solve the first equation for

Substitute in the **other** equation, to get:

so we want

What happened?

The way substitution works is to suppose we have an

When we get

Every solution to the first equation **already is** a solution to the second. There is **no additional** requirement.

If you think about the lines we'd get if we graphed these 2 equations, you'll see that they are the same line. Every point on one line is a point of the other line.

OK there's only **one line** so it might be better to say: every solution to one equation is a solution to the other.

There are a couple of ways to write the solution:

we can say "the system is dependent"

of, course that doesn't really say what the solutions are.

Every solution to the first equation,

Often, we like to do things by first choosing

so

We can now write the solutions:

**Final note**

If you write both equations in slope-intercept form:

you'll get

(That's one reason we like slope-intercept form.)