Problem 2 - College Algebra

Question

Determine whether the given ordered pair is a solution of the system. \((-3,5)\) \(\left\\{\begin{array}{l}9 x+7 y=8 \\ 8 x-9 y=-69\end{array}\right.\)

Step-by-Step Solution

Answer

Yes, the ordered pair \(-3,5\) is a solution to the system of equations.

Step 1: Substitute x and y values into equation 1

Take the first equation \(9x+7y=8\) and substitute \(x=-3\) and \(y=5\). This results in \(9(-3)+7(5)=8\).

Step 2: Check if equation 1 is true

Upon calculating the left side of the equation, we get \(-27+35=8\), which simplifies to \(8=8\). So, the ordered pair \(-3,5\) satisfies the first equation.

Step 3: Substitute x and y values into equation 2

Now take the second equation \(8x-9y=-69\) and substitute \(x=-3\) and \(y=5\). This results in \(8(-3)-9(5)=-69\).

Step 4: Check if equation 2 is true

Upon calculating the left side of the equation, we get \(-24-45=-69\), which simplifies to \(-69=-69\). So, the ordered pair \(-3,5\) satisfies the second equation as well.