How Do I Solve for x and y Using Simultaneous Equations?

[MadmanMurray]

Crazy Simultaneous Equation ?!?

Homework Statement

Solve for x and y
1)2x - 3y = 1
2)x² - 2xy - 3y² = -3

Homework Equations

The Attempt at a Solution

I substituted the linear equation into the quadratic and got a quadratic with only y in it:
3.) 15y² - 2y = 13

I then substituted the linear into eq3 and got a quadratic with only x in it:
4.) 5x² - 6x = 9

Do I need substitute that linear into these quadratics twice more so I get 2 simultaneous quadratics with only x in them and 2 quadratics with only y in them?

I've been on this question for about half an hour now but this is a sample question from a test so there's no way I could spend that long on a single question on a test. I must be doing it wrong.

 

[rootX]

where is eqn 3?
You say it has only y in it why aren't you solving it then?

 

[MadmanMurray]

Its a quadratic if has y^2 and y. I'll edit the post and put in all the equations I got

 

[Delphi51]

3.) 15y2 - 2y = 13

Looks good! The rest is easy - just use one of your techniques for solving a quadratic equation to find the number(s) for y.

 

[MadmanMurray]

Ah yea I didn't even think of factorizing or anything like that. Thanks.