Algebra

Systems of Equations

System of Equations - Elimination

         

If x,yx, y are distinct values satisfying x2=21x+12yx^2 = 21x + 12 y and y2=21y+12xy^2 = 21 y + 12 x, what is the value of x2+y2x^2 + y^2 ?

What positive integer value of MM satisfies the following system of equations:

{M+N=25MN=175? \begin{cases} \sqrt{M} + \sqrt{N} = 25 \\ M - N = 175 ? \\ \end{cases}

Let aa and bb be the values of real numbers xx and yy, respectively, that satisfy x2xy+y2=3,x2+y2=5.x^2-xy+y^2=3, x^2+y^2=5. What is the value of a+b?\lvert{a+b}\rvert?

Suppose xx and yy satisfy both of the nonlinear equations {x3+y3=62x2xy+y2=31. \begin{cases} x^3 + y^3 & = 62 \\ x^2 - xy + y^2 & = 31. \end{cases} Find xy xy .

If x=a  (>0)x=a \; (> 0) and y=by=b are solutions of the simultaneous equations 9x210xy+y2=0,5x2y2=64, 9x^2-10xy+y^2=0,\, 5x^2-y^2=64, what is the value of a+ba+b?

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