Question

Which of the following points is a solution to the system of equations shown?

y - x = -1
x + y = -5

(-3, -2)
(-6, 1)
(-2, -3)

Answer 1

The point that satisfies both equations y - x = -1 and x + y = -5 in the system of equations is (-2, -3). We verified this by substituting the coordinates of each point into both equations and confirming both are true only for (-2, -3).

Step-by-step explanation:

The student is asking which of the following points is a solution to the given system of equations:

• y - x = -1
• x + y = -5

To find the solution, we need to determine which point satisfies both equations simultaneously. We substitute the x and y values of each point into both equations and check for equality.

For the point (-3, -2):

• Substituting into the first equation: (-2) - (-3) = 1, which is not equal to -1.
• Substituting into the second equation: (-3) + (-2) = -5, which is equal to -5.

For the point (-6, 1):

• Substituting into the first equation: 1 - (-6) = 7, which is not equal to -1.
• Substituting into the second equation: (-6) + 1 = -5, which is equal to -5.

For the point (-2, -3):

• Substituting into the first equation: (-3) - (-2) = -1, which is equal to -1.
• Substituting into the second equation: (-2) + (-3) = -5, which is equal to -5.

Hence, the point that satisfies both equations is (-2, -3), making it the correct solution to the system.

Answer 2

The coordinate points would be (-2,-3).