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Chapter 4: Problem 8

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(8,5)\\\&\left\\{\begin{aligned}5 x-4 y &=20 \\\3 y &=2 x+1\end{aligned}\right.\end{aligned}$$

Short Answer

Expert verified
The ordered pair (8,5) is not a solution to the system of equations.

Step by step solution

01

Substitute into the first equation

For the first equation \(5x - 4y = 20\), replace \(x\) with 8 and \(y\) with 5. The resulting equation is \(5*8 - 4*5 = 20\), which simplifies to \(40 - 20 = 20\). This is a true statement, so the ordered pair is a solution for the first equation.
02

Substitute into the second equation

For the second equation \(3y = 2x + 1\), replace \(x\) with 8 and \(y\) with 5. The resulting equation is \(3*5 = 2*8 + 1\), which simplifies to \(15 = 16 + 1\). This is not a true statement.
03

Conclusion

Since the ordered pair does not satisfy the second equation, we can conclude that the ordered pair (8,5) is not a solution to this system of equations.

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