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Excel in math and science
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It's hard to learn from lectures and videos
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System of Linear Equations
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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
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
Consider a system of linear equations \[\begin{align} x+y &= 3, \\ y+z &= 11, \\ z+x &= 20. \end{align}\] What is the value of \(3x+y+5z\)?
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
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(x=a\), \(y=b\) and \(z=c\) be the values of \(x\), \(y\) and \(z\), respectively, that satisfy the system of linear equations \[ \begin{align} x-y&=3 \\ y+z&=25 \\ z-x&=8. \end{align}\] What is the value of \(a+b+c\)?
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
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(x=a\), \(y=b\) and \(z=c\) be the values of \(x\), \(y\) and \(z\), respectively, that satisfy the system of linear equations \[ \begin{align} x+2y&= 24 \\ 2y+3z&= 58\\ x+3z&= 38. \end{align}\] What is the value of \(a+b+c\)?
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
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(x=a\), \(y=b\) and \(z=c\) be the values of \(x\), \(y\) and \(z\), respectively, that satisfy the system of linear equations \[ \frac{3-x}{2}= \frac{y+1}{3}=\frac{2z-1}{5}, \, 3x+2y+z=65. \] What is the value of \(a+b+c\)?
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
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(x=A\), \(y=B\) and \(z=C\) be the solutions of the simultaneous equations \[\begin{align} x+y+z &= 270 \\ x-y+z &= 90 \\ x+y-z &=0. \end{align}\] What is the value of \(\frac{A+B}{C}\)?