How do you solve the system of equations #2x-5y=23# and #3x+7y=-9# by linear combination?

1 Answer
Lorenzo D.
May 30, 2017

1)Multiply the second equation by 2
2)Subtract the first equation to the second equation multiplyed by 3

Explanation:

It's not the smartest method but there we go:
your aim is to add or subtract one equation to the other to delete #x# or #y# so that will be easier to find the other variable.
That's the process:
1)
#2*(3x+7y)=2*(-9)rarr6x+14y=-18#
2) #(6x+14y)-3(2x-5y)=-18-(3*23)rarrcancel(6x)+14y-cancel(6x)+15y=-18-69rarr29y=-87rarry=-(87/29)=-3#
3)
now that you have #y# just calculate #x# from the first equation:
#2x-5*(-3)=23rarr2x=8rarrx=(8/2)rarrx=4#

So the solution is #(x,y)=(4,-3)#

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