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Converting linear equations to slope-intercept form

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Write the two equations in slope-intercept form, and then determine how many solutions the system has.

x - 3y = 6
3y + 1 = x

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I'm going to give a lot of detail, so that you can quickly read the things you already know, and focus on the things you don't. These are linear equations, meaning each one is an equation for a line. The slope-intercept form of a linear equation is like this:

y = mx + b

where m is the slope, and b is the intercept. An example would be y = 5x + 2, where the slope is 5 and the intercept is 2. What we need to do is rearrange the equations so that:

1. Only y is on the left-hand side of the equals sign,
2. There is one x term on the right-hand side, and it's the first thing on the right-hand side, and
3. There is one term that's just a number (called a "constant term") on the right-hand side, added after the x term.

So let's get started. Take the first equation, and apply rule 1 by subtracting x from both sides. Remember the rules of what we can do to equations: we can add, subtract, multiply, or divide by something, but we have to do it to both sides of the equation.

x - 3y = 6
x - 3y - x = 6 - x
-3y = -x + 6

Note that I canceled the x and the subtracted x (x - x is 0, and there's no need to keep the 0 around and keep writing 0 - 3y). I also moved the - sign to be next ...

Solution Summary

Using two examples, shows how to take a linear equation in x and y and put it in slope-intercept form. Also shows how to determine how many solutions that system of two equations has.