Difference between revisions of "2018 AMC 10A Problems/Problem 12"

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How many ordered pairs of real numbers <math>(x,y)</math> satisfy the following system of equations?
 
How many ordered pairs of real numbers <math>(x,y)</math> satisfy the following system of equations?
\begin{align*}x+3y&=3\\ \big||x|-|y|\big|&=1\end{align*}
+
<math>x+3y=3 \ \big||x|-|y|\big|=1</math>
 
<math>\textbf{(A) } 1 \qquad  
 
<math>\textbf{(A) } 1 \qquad  
 
\textbf{(B) } 2 \qquad  
 
\textbf{(B) } 2 \qquad  

Revision as of 15:38, 8 February 2018

How many ordered pairs of real numbers $(x,y)$ satisfy the following system of equations? $x+3y=3 \ \big||x|-|y|\big|=1$ $\textbf{(A) } 1 \qquad  \textbf{(B) } 2 \qquad  \textbf{(C) } 3 \qquad  \textbf{(D) } 4 \qquad  \textbf{(E) } 8$

See Also

2018 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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