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Excel in math and science
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Algebra
Systems of Equations
Excel in math and science
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It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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Concept Quizzes
If \(x, y \) are distinct values satisfying \(x^2 = 21x + 12 y\) and \(y^2 = 21 y + 12 x\), what is the value of \(x^2 + y^2 \)?
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
What positive integer value of \(M \) satisfies the following system of equations:
\[ \begin{cases} \sqrt{M} + \sqrt{N} = 25 \\ M - N = 175 ? \\ \end{cases} \]
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
Let \(a\) and \(b\) be the values of real numbers \(x\) and \(y\), respectively, that satisfy \[x^2-xy+y^2=3, x^2+y^2=5.\] What is the value of \(\lvert{a+b}\rvert?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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by Brilliant Staff
Suppose \(x\) and \(y\) satisfy both of the nonlinear equations \[ \begin{cases} x^3 + y^3 & = 62 \\ x^2 - xy + y^2 & = 31. \end{cases} \] Find \( xy \).
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
If \(x=a \; (> 0)\) and \(y=b\) are solutions of the simultaneous equations \[ 9x^2-10xy+y^2=0,\, 5x^2-y^2=64,\] what is the value of \(a+b\)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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including olympiad champions, researchers, and professionals.
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by Brilliant Staff