Where do the lines #3x + y = 9# and #4x + 2y = 6# intersect?

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Answer 1 · 2017-01-26T04:30:27

The solution is #(6, -9)#.

You need to start by isolating one of the variables. Usually, if one of the variables has coefficient #1#, then this will be easiest to isolate.

#3x + y = 9 -> y = 9 - 3x#

Substitute this into the other equation now for #y#, leaving only x's.

#4x + 2(9 - 3x) = 6#

#4x + 18 - 6x = 6#

#-2x = -12#

#x = 6#

Now insert #x = 6# into one of the equations to solve for #y#.

#3(6) + y = 9#

#y = 9 - 18#

#y = -9#

The intersection point of the two lines is therefore #(6, -9)#. Remember: when graphing, points are always listed in the form #(x, y)#.

Hopefully this helps!