How do you find the solution of the system of equations #2x – y = 4 # and #3x + y = 1 #?

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Answer 1 · 2015-05-02T07:20:56

We can add the two equations to eliminate #y#

Adding the 2 equations will give us:

#(2x-y) +(3x + y) = 4+ 1#

#2x - cancel(y) + 3x + cancel(y) = 5#

#5x = 5#

Dividing both sides by 5 gives us

#(cancel(5)x)/cancel(5) = cancel(5)/cancel(5)#

#color(green)(x = 1#

Now we can substitute #x =1# in the second equation to get #y#

#3*1 + y = 1#

#3 + y = 1#

Subtracting 3 from both sides will give us:

#cancel(3) + y - cancel(3) = 1 - 3#

# color(green)(y = -2#

The solution to these system of equations is:

#color(green)(x = 1 ; y = -2#