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What is x and y in the system of equations 3x + 2y = 170 and 4x + 6y = 360

 May 23, 2020
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What is x and y in the system of equations 3x + 2y = 170 and 4x + 6y = 360?

 

One way to solve this is by "linear combinations" --  getting either the x-term or the y-term in

both equations to be the same and then either add or subtract.

 

I'm going to make the y-term (2y) of the first equation to be the same as the y-term of the second

equation (6y) by multiplying the first equation by 3:

 

3x + 2y  =  170   --->   multiply by 3   --->   9x + 6y  =  510

4x + 6y  =  360                                            4x + 6y  =  360

subtract down the columns:                        5x          =  150

divide by 5:                                                            x  =  30

 

Now, substitute that value back into the first equation:

     3x + 2y  =  170   --->   3(30) + 2y  =  170   --->   90 + 2y  =  170

                                                                                         2y  =    80

                                                                                           y  =  40

 May 23, 2020

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