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:

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