How do you write this system of equations in matrix form?

x²+y²=17
x+y=5

Question

How do you write this system of equations in matrix form?

x²+y²=17
x+y=5

anonymous · Answer

I tried this, but that can't be right:
[ 1  1  |  17 ]
[ 1  1  |    5 ]

owlcoffee · Answer

I might be wrong on this one but:
$$x^2+y^2=17$$
$$x+y=5$$
Then:
$$x.x+y.y=17$$
$$x+y=5$$
$$\iff \left[\begin{matrix}x & y & 17 \ 1 & 1 & 5\end{matrix}\right]$$

owlcoffee · Answer

Are we speaking about Cramers method of reduction?

anonymous · Answer

Hmm, no, not Cramers. Gauss-Jordan's elimination actually.

trojanpoem · Answer

Gauss elimination works with linear equations and the second one isn't , so somehow we have to turn it into one

trojanpoem · Answer

x²+y²=17 <<< if it was x^2 - y^2 

It would have been easier.

anonymous · Answer

Certain. I solved it using regular algebra, the results were 1 and 4. Was just wondering if it's possible using linear algebra too.

trojanpoem · Answer

HOw about this ?

(x+y) ^2 = 25

x^2 + y^2 + 2xy = 25

let x^2 = t , y^2 = k , xy = c

t + k + 2c = 25 -> first eqn

x^2+y^2 = 17

t + k = 17 -> 2nd

trojanpoem · Answer

Now we can put it into a matrix.

trojanpoem · Answer

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