Answered

Get insightful responses to your questions quickly and easily on IDNLearn.com. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

The solution to a system of linear equations is [tex][tex]$(-3,-3)$[/tex][/tex]. Which system of linear equations has this point as its solution?

A. [tex][tex]$x - 5y = -12$[/tex][/tex] and [tex][tex]$3x + 2y = -15$[/tex][/tex]
B. [tex][tex]$x - 5y = -12$[/tex][/tex] and [tex][tex]$3x + 2y = 15$[/tex][/tex]
C. [tex][tex]$x - 5y = 12$[/tex][/tex] and [tex][tex]$3x + 2y = -15$[/tex][/tex]
D. [tex][tex]$x - 5y = 12$[/tex][/tex] and [tex][tex]$3x + 2y = 15$[/tex][/tex]

Sagot :

GinnyAnsweridn
To determine which system of linear equations has the point [tex]\((-3, -3)\)[/tex] as its solution, we need to substitute [tex]\((x, y) = (-3, -3)\)[/tex] into each pair of equations. We will then verify if both equations in any system are satisfied by this point.

Let's analyze each system one by one:

### System 1:
[tex]\[ x - 5y = -12 \][/tex]
[tex]\[ 3x + 2y = -15 \][/tex]

Substitute [tex]\((x, y) = (-3, -3)\)[/tex]:
1. For the first equation:
[tex]\[ -3 - 5(-3) = -3 + 15 = 12 \neq -12 \][/tex]
The point [tex]\((-3, -3)\)[/tex] does not satisfy the first equation. Therefore, this system cannot be the answer.

### System 2:
[tex]\[ x - 5y = -12 \][/tex]
[tex]\[ 3x + 2y = 15 \][/tex]

Substitute [tex]\((x, y) = (-3, -3)\)[/tex]:
1. For the first equation:
[tex]\[ -3 - 5(-3) = -3 + 15 = 12 \neq -12 \][/tex]
The point [tex]\((-3, -3)\)[/tex] does not satisfy the first equation. Therefore, this system cannot be the answer.

### System 3:
[tex]\[ x - 5y = 12 \][/tex]
[tex]\[ 3x + 2y = -15 \][/tex]

Substitute [tex]\((x, y) = (-3, -3)\)[/tex]:
1. For the first equation:
[tex]\[ -3 - 5(-3) = -3 + 15 = 12 \][/tex]
The point [tex]\((-3, -3)\)[/tex] satisfies the first equation.
2. For the second equation:
[tex]\[ 3(-3) + 2(-3) = -9 - 6 = -15 \][/tex]
The point [tex]\((-3, -3)\)[/tex] satisfies the second equation.

Since the point [tex]\((-3, -3)\)[/tex] satisfies both equations, this system could be the correct one.

### System 4:
[tex]\[ x - 5y = 12 \][/tex]
[tex]\[ 3x + 2y = 15 \][/tex]

Substitute [tex]\((x, y) = (-3, -3)\)[/tex]:
1. For the first equation:
[tex]\[ -3 - 5(-3) = -3 + 15 = 12 \][/tex]
The point [tex]\((-3, -3)\)[/tex] satisfies the first equation.
2. For the second equation:
[tex]\[ 3(-3) + 2(-3) = -9 - 6 = -15 \neq 15 \][/tex]
The point [tex]\((-3, -3)\)[/tex] does not satisfy the second equation. Therefore, this system cannot be the answer.

After substituting the point [tex]\((-3, -3)\)[/tex] into each system of equations, we find that the only system that satisfies both equations is:

[tex]\[ \boxed{ x - 5y = 12 \text{ and } 3x + 2y = -15 } \][/tex]

This corresponds to the third system of linear equations.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.