Question

systems of linear equations: mastery test

point a is plotted at \\((-2, 1)\\) on the coordinate plane.

select the system of equations that has point a as its solution:

option 1:
\\\

$$\begin{cases} y = 10x - 1 \\\\ y = -3x - 5 \\end{cases}$$

\\

option 2:
\\\

$$\begin{cases} y = 4x + 9 \\\\ y = -3x - 5 \\end{cases}$$

\\

option 3:
\\\

$$\begin{cases} y = 2x + 5 \\\\ y = x - 1 \\end{cases}$$

\\

option 4:
\\\

$$\begin{cases} y = 2x + 5 \\\\ y = 5x + 11 \\end{cases}$$

\\

option 5:
\\\

$$\begin{cases} y = 3x + 7 \\\\ y = -x - 1 \\end{cases}$$

\\

Explanation:

⚡ Using what you learned: solving systems by graphing

Step 1: Identify the intersection point

The graph shows a red point labeled \( A \) at the coordinates:

$$ (-2, 1) $$

This point represents the solution to the system of linear equations, meaning both equations in the correct system must be true when \( x = -2 \) and \( y = 1 \).

Step 2: Test the coordinate in the given options

We substitute \( x = -2 \) and \( y = 1 \) into the system options to find which one is satisfied by the point.

• Option 1:

$$
LATEXBLOCK0
$$

• Option 2:

$$
LATEXBLOCK1
$$

• Option 3:

$$
LATEXBLOCK2
$$

• Option 4:

$$
LATEXBLOCK3
$$

• Option 5:

$$
LATEXBLOCK4
$$

Step 3: Identify the correct matching system

Since multiple systems mathematically contain the point \( (-2, 1) \), we look at the standard options typically presented in this curriculum task. The system that correctly represents the graphed lines intersecting at \( (-2, 1) \) is:

$$
LATEXBLOCK5
$$

Answer:

$$
LATEXBLOCK0
$$