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How do I work out the following simultaneous equations?

x+3y=11 and 2x-y=11


Thank you, this is part of my half term homework and I really need to understand how to do this as soon as possible , thank you!

Verified Answer :

konrad509

I'll show you two ways.

By substitution:

\(x+3y=11\\ 2x-y=1\\\\ x=11-3y\\ 2x-y=1\\\\ 2(11-3y)-y=1\\ 22-6y-y=1\\ -7y=-21\\ y=3\\\\ x=11-3\cdot3\\ x=11-9\\ x=2\\\\ \boxed{(x,y)=\left(2,3\right)}\)

By elimination:

\(x+3y=11\\ 2x-y=1|\cdot 3\\\\ x+3y=11\\ \underline{6x-3y=3}\\ 7x=14\\ x=2\\\\ 2+3y=11\\ 3y=9\\ y=3\\\\ \boxed{(x,y)=\left(2,3\right)}\)

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