Mcguire Bradley
01/26/2023 · Elementary School
A student determined that the ordered pair \( (3,-5) \) is a solution of the following system. \[ \begin{array}{r}4 x+y=4 \\ x+y=-2\end{array} \] His reasoning was that the ordered pair satisfies the second equation \( x+y=-2 \), since \( 3+(-5)=-2 \). What went wrong?
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The student's error was in checking only one equation. An ordered pair must satisfy all equations in a system to be a solution. The ordered pair \( (3, -5) \) does not satisfy the first equation, so it is not a solution to the system.
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