How do you solve 2x+5y=3 and x-3y=7?

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Answer 1 · 2015-09-28T09:27:41

The system has a solution:

#{(x=4),(y=-1):}#

#{(2x+5y=3),(x-3y=7):}#

First we multiply the second equation by #-2#

#{(2x+5y=3),(-2x+6y=-14):}#

Now we can add the equations to get an equation with one unknown only:

#11y=-11#

Now we can calculate, that #y=-1#

If we substitute the value of #y# to the 2nd equation we get:

#x+3=7#

So #x=4#

Finally we can write the solution:

#{(x=4),(y=-1):}#