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Chapter 7: Problem 1

In Exercises 1-4, determine whether the given ordered pair is a solution of the system. \((2,3)\) \(\left\\{\begin{array}{l}x+3 y=11 \\ x-5 y=-13\end{array}\right.\)

Short Answer

Expert verified
Yes, the ordered pair (2,3) is indeed the solution of the system of equations.

Step by step solution

01

Analyze the equation and plug in the values for x and y

The first equation in the system is \(x + 3y = 11\). To see if the ordered pair \( (2,3) \) is a solution, substitute \(x = 2\) and \(y = 3\) into the equation. It becomes \(2 + 3(3) = 2+ 9 = 11\), which is true. So, the ordered pair satisfies the first equation.
02

Verify the solution with the second equation

The second part of the system is \(x 鈥� 5y = -13\). Plug \(x = 2\), \(y = 3\) into the second equation. It becomes \(2 - 5(3) = 2 - 15 = -13\), which is true. This means the ordered pair also satisfies the second equation.
03

Solutions

Since the ordered pair satisfies both equations, we can say that it is a solution to the system of equations.

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