SOLUTION: Solve each system by the addition method. Determine whether the equations are independent, dependent, or inconsistent x-y= 3 -6x+6y=17

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Question 246064: Solve each system by the addition method. Determine whether
the equations are independent, dependent, or inconsistent
x-y= 3
-6x+6y=17
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
equations are:

x-y = 3
-6x+6y = 17

multiply first equation by 6 to get:

6x-6y = 18

add to second equation to get:

6x-6y = 18
plus
-6x+6y = 17
equals
0 + 0 = 35

this becomes 0 = 35 which is false.

there is no common solution to this system of equations.

Here's a definition of independent, dependent, or inconsistent.

If you have 1 valid solution then the equations are independent.

If you have multiple valid solutions, then the equations are dependent.

If you have 0 valid solutions then the solution are inconsistent.

These equations are inconsistent.

If we graphed this solution, we would find the lines are parallel.

Another way is to convert the equations to slope-intercept form and see if the slopes are the same.

If they are, the lines are parallel.

Your first equation is x-y = 3

Convert to slope-intercept form and you get y = x-3 meaning the slope is 1.

Your second equation is -6x + 6y = 17

Convert to slope-intercept form and you get y = x + 17/6 meaning the slope is 1.

The slopes are the same so the lines are parallel meaning they will never intercept meaning the solution is inconsistent.

A graph of these two equations is shown below: