Question

Consider the following system of equations:

Line 1: x + y = -2
Line 2: 3x - y = 2
Now, analyze the system of equations.

A) The ordered pair [-4,2] is a solution to this system.
B) The ordered pair [2,4] is a solution to this system.
C) The ordered pair [0,-2] is a solution to this system.
D) The solution to this system of equations represents:

A) The intersection of two lines in a coordinate plane.
B) A real-world problem involving x and y.
C) The sum of two numbers.
D) The result of multiplying x and y.

Answer 1

The correct ordered pair that is a solution to the given system of equations is [0,-2], and the solution represents the intersection of two lines in a coordinate plane.

Step-by-step explanation:

Analysis of the System of Equations

For the system of equations given:

• Line 1: x + y = -2
• Line 2: 3x - y = 2

We will assess each of the provided ordered pairs to determine if they are solutions to the system.

To verify each option:

1. Substitute the x and y values from the ordered pair into both equations.
2. Check if both equations are true simultaneously.

Verification of ordered pairs:

• A) For [-4,2], checking Line 1: (-4) + 2 ≠ -2 and Line 2: 3(-4) - 2 ≠ 2. Thus, it is not a solution.
• B) For [2,4], checking Line 1: 2 + 4 ≠ -2 and Line 2: 3(2) - 4 ≠ 2. It is not a solution either.
• C) For [0,-2], checking Line 1: 0 - 2 = -2 and Line 2: 3(0) + 2 = 2. Both equations are true, so this is a solution.

As for part D) The solution to this system of equations represents:

• The intersection of two lines in a coordinate plane.