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Solve the following system of linear equations by graphing:22--- 3x + y- 9x + 3y66

Solve the following system of linear equations by graphing:22--- 3x + y- 9x + 3y66-example-1
User Nkirkes
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1 Answer

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Let's start by rewriting the given equations in slope-intercept form, this way we can have a first look and see if the equations represent the same line, and then an infinite number of solutions are present.

We can rewrite the equations in slope-intercept form by solving for y, like this:

For the first equation, -3x + y = 22:

-3x + y = 22

-3x + 3x + y = 22 + 3x

y = 22 + 3x

y = 3x + 22

For the second equation, -9x + 3y = 66

-9x + 3y = 66

-9x + 9x + 3y = 66 + 9x

3y = 66 + 9x

3y/3 = 66/3 + 9x/3

y = 22 + 3x

y = 3x + 22

As you can see, both equations look the same (y = 3x + 22) in slope-intercept form. Since they represent the same line the system of linear equations will have an infinite number of solutions.

User Martin Osusky
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