To determine which ordered pair is a solution to the given system of linear equations, we need to check each pair against both equations. The system of equations is:
1. [tex]\( x + 2y = 3 \)[/tex]
2. [tex]\( y = -2x - 3 \)[/tex]
Let's examine each given ordered pair to see which one satisfies both equations:
### Pair (-3, -3)
1. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = -3 \)[/tex] into the first equation:
[tex]\[
-3 + 2(-3) = -3 - 6 = -9 \neq 3
\][/tex]
Therefore, (-3, -3) does not satisfy the first equation.
### Pair (3, 3)
1. Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 3 \)[/tex] into the first equation:
[tex]\[
3 + 2(3) = 3 + 6 = 9 \neq 3
\][/tex]
Therefore, (3, 3) does not satisfy the first equation.
### Pair (3, -3)
1. Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = -3 \)[/tex] into the first equation:
[tex]\[
3 + 2(-3) = 3 - 6 = -3 \neq 3
\][/tex]
Therefore, (3, -3) does not satisfy the first equation.
### Pair (-3, 3)
1. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 3 \)[/tex] into the first equation:
[tex]\[
-3 + 2(3) = -3 + 6 = 3
\][/tex]
The first equation is satisfied.
2. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 3 \)[/tex] into the second equation:
[tex]\[
y = -2(-3) - 3 = 6 - 3 = 3
\][/tex]
The second equation is also satisfied.
Since the ordered pair [tex]\((-3, 3)\)[/tex] satisfies both equations in the system, it is the solution to the system. Therefore, the correct ordered pair is:
[tex]\[
(-3, 3)
\][/tex]
