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# Systems of Equations

Vieta root jumping is a descent method that occurs when you have to solve a Diophantine equation whose solutions have a recursive structure. Popular in advanced math olympiad number theory problems.

# System of Equations: Level 2 Challenges

$\begin{cases} { x }^{ 2 }+{ y }^{ 2 }=30 \\ x+y=10 \end{cases}$

If the above equations are true simultaneously, then find the value of $$xy$$.

$\large \begin{cases} { a(b+c)=32 } \\ { b(c+a) = 65 } \\ {c(a+b) = 77 } \end{cases}$

Given that $$a , b,$$ and $$c$$ are positive real numbers that satisfy the system of equations above, find the value of $$abc$$.

Given that ${ a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }+{ d }^{ 2 }=1$ And also that $$ac+bd=0$$ What is the value of $$ab+cd$$?

For the positive numbers $$d, o, v, e$$: $d^2 + do = 250 \\ o^2 + do = 150$ $v^2 + ve = 30 \\ e^2 + ve = 34$ Find the value of $$d + o + v + e$$.

You think you rock at linear equation? Gimme the solution NOT using hit and trial method! Solve for the values of "x" and "y" and enter $$x+y$$

Note: These are not linear equations.

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