Question

**i can determine if an ordered pair is a solution to a system. determine if the ordered pair is a solution of the system or not. justify your answer by showing your work. 27. ( y = x - 4 ) ( y = -3x ) ( (1, -3) ) 28. ( y = x + 20 ) ( y = 6x ) ( (-4, 24) )

Explanation:

Problem 28: Determine if \((-4, 24)\) is a solution to the system \(

$$\begin{cases} y = x + 20 \\ y = 6x \end{cases}$$

\)

Step 1: Check the first equation \(y = x + 20\)

Substitute \(x = -4\) and \(y = 24\) into the equation.
Left - hand side (LHS) \(= y = 24\)
Right - hand side (RHS) \(= x + 20=-4 + 20 = 16\)
Since \(24
eq16\), we can already tell that the ordered pair does not satisfy the first equation. But for thoroughness, we can also check the second equation.

Step 2: Check the second equation \(y = 6x\)

Substitute \(x=-4\) and \(y = 24\) into the equation.
LHS \(= y=24\)
RHS \(=6x=6\times(-4)=-24\)
Since \(24
eq - 24\), the ordered pair does not satisfy the second equation either.

Answer:

The ordered pair \((-4,24)\) is not a solution to the system \(

$$\begin{cases}y = x + 20\\y=6x\end{cases}$$

\)