SOLUTION: Solve the simultaneous equation 2x-3y=17 and x^2+2y^2-3x+y=19

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Question 1131367: Solve the simultaneous equation
2x-3y=17 and x^2+2y^2-3x+y=19
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
From the first equation, express  x =   and substitute it into the second equation.


Then you will get a single quadratic equation for "y", which you can solve by either way.


After solving it and obtaining the solution for "y", restore the corresponding value for x.

That's all.

-------------------

To see many solved similar problems (yours TEMPLATES and SAMPLES), look into the lesson
    - Solving systems of algebraic equations of degree 2 and degree 1
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of equations that are not linear".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
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to your archive and use it when it is needed.


Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
2x=3y+17
x=(3/2)y+8.5
(9/4)y^2+25.5y+72.25+2y^2-4.5y-25.5+y=19
4.25y^2+22y+27.75y=0
17y^2+88y+111=0
y=(1/34)(-88+/- sqrt (88^2-4(17*111)); sqrt term= sqrt(196)=14
y=-74/34 or -2.18
2x+6.54=17 and x=5.23
substitute into second and 27.35+9.51-15.69-2.18=18.99, checks given rounding error.
exact values are
2x+111/17=289/17
x=89/17, y=-89/17,
(89/17, -37/17)

y=-102/34 or -3
y=-3 and 2x+9=17 and x=4
substitute into second equation and 16+18-12-3=19
(4, -3)
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