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. $y = x + 20$ $y = 6x$ $(-4, 24)$ 29. $y = -x - 4$ $y = x$ $(2, -2)$ 30. $y = x - 6$ $y = 2x$ $(-6, -12)$

Explanation:

Problem 29: Determine if \((2, -2)\) is a solution to the system \(

$$\begin{cases}y = -x - 4\\y = x\end{cases}$$

\)

Step 1: Substitute into the first equation

Substitute \(x = 2\) and \(y = -2\) into \(y = -x - 4\).
Left - hand side (LHS) \(= y=-2\)
Right - hand side (RHS) \(=-x - 4=-2 - 4=-6\)
Since \(-2
eq - 6\), the ordered pair does not satisfy the first equation. But we can also check the second equation for completeness.

Step 2: Substitute into the second equation

Substitute \(x = 2\) and \(y=-2\) into \(y = x\)
LHS \(=y = - 2\), RHS \(=x = 2\)
Since \(-2
eq2\), the ordered pair does not satisfy the second equation either.

Problem 30: Determine if \((-6,-12)\) is a solution to the system \(

$$\begin{cases}y=x - 6\\y = 2x\end{cases}$$

\)

Step 1: Substitute into the first equation

Substitute \(x=-6\) and \(y = - 12\) into \(y=x - 6\)
LHS \(=y=-12\)
RHS \(=x - 6=-6-6=-12\)
The ordered pair satisfies the first equation.

Step 2: Substitute into the second equation

Substitute \(x = - 6\) and \(y=-12\) into \(y = 2x\)
LHS \(=y=-12\)
RHS \(=2x=2\times(-6)=-12\)
The ordered pair satisfies the second equation.

Answer:

s:

• For problem 29: The ordered pair \((2,-2)\) is not a solution to the system \(

$$\begin{cases}y=-x - 4\\y = x\end{cases}$$

\)

• For problem 30: The ordered pair \((-6,-12)\) is a solution to the system \(

$$\begin{cases}y=x - 6\\y = 2x\end{cases}$$

\)