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Chapter 5: Problem 2

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

Short Answer

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

Step by step solution

01

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 \(9(-3)+7(5)=8\).
02

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.
03

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 \(8(-3)-9(5)=-69\).
04

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.

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Most popular questions from this chapter

Solve the systems $$\left\\{\begin{array}{l} \log _{y} x-3 \\ \log _{y}(4 x)-5 \end{array}\right.$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$\frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2}$$

What is a system of linear inequalities?

Without graphing, in Exercises 73鈥�76, determine if each system has no solution or infinitely many solutions. $$\left\\{\begin{array}{l} (x+4)^{2}+(y-3)^{2} \leq 9 \\ (x+4)^{2}+(y-3)^{2} \geq 9 \end{array}\right.$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Partial fraction decomposition involves finding a single rational expression for a given sum or difference of rational expressions.
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