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Chapter 7: Problem 3

Determine whether the given ordered pair is a solution of the system. \((2,5)\) \(\left\\{\begin{array}{r}2 x+3 y=17 \\ x+4 y=16\end{array}\right.\)

Short Answer

Expert verified
The ordered pair (2,5) is not a solution to the system of equations.

Step by step solution

01

Substitute the Ordered Pair into the First Equation

Substitute \(x =2\) and \(y =5\) into the first equation \(2x+3y=17\). So it becomes \(2(2) + 3(5) = 17\). Evaluating the expressions on the left hand side, this statement becomes \(4 + 15 = 17\), which simplifies to \(19 = 17\). This statement is not true, therefore the ordered pair (2,5) is not a solution of the first equation.
02

Substitute the Ordered Pair into the Second Equation

Substitute \(x =2\) and \(y =5\) into the second equation \(x+4y=16\). So it becomes \(2 + 4(5) = 16\). Evaluating the expressions on the left hand side, this statement becomes \(2 + 20 = 16\), which simplifies to \(22 = 16\). This statement is not true, therefore the ordered pair (2,5) is not a solution of the second equation.
03

Conclusion

Since the ordered pair (2,5) does not satisfy either equation in the system, we can conclude that (2,5) is not a solution to the system of equations.

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