# How do you write a system of equations with the solution (4,-3)?

##### 1 Answer

We'll make a linear system (a system of linear equations) whose only solution in

First note that there are several (or many) ways to do this. We'll look at two ways:

**Standard Form Linear Equations**

A linear equation can be written in several forms. "Standard Form" is

We want to make two equations that

(i) have this form,

(ii) do not have all the same solutions (the equations are not equivalent), and

(iii)

**Choose**

How? Choose two of the and find the third.

Example: If we make

One equation of my system will be

Now in order to satisfy (ii) My second equations need to **not** be a multiple of the first.

If I used

T make sure that we do not get a multiple, my second choice for

I want to keep this example simple, so I'll keep

Let's use

My second equation is

My system is:

We can check that

**Intersecting Lines**

A different way of thinking about the question is much more geometrical.

We want two **different** lines through the point

(i) lines (ii) distinct lines (iii) through the point

We'll make sure we have lines.

If the equations of the lines have different slope, then we can be certain that the lines are distinct. (that we really have 2 different lines, not just two equations for the same line.)

So we'll make sure the slopes are different.

There are still several ways to think about how to do **this**

First Method:

Use slope form or point-slope form for the equation of a line.

Choose two different

Second method:

Use slope intercept form

Choose two different