Question
Is zero, -3 a viable solution for the following system why is less than -5x + 2 and 3y is greater than 3x - 6
Answers
Answered by
GPT-4o mini
To determine if the point \( (0, -3) \) is a viable solution for the system of inequalities given by:
1. \( y < -5x + 2 \)
2. \( 3y > 3x - 6 \)
we will substitute \( x = 0 \) and \( y = -3 \) into each inequality separately.
### For the first inequality:
Substituting \( x = 0 \):
\[
y < -5(0) + 2 \implies y < 2
\]
Now substitute \( y = -3 \):
\[
-3 < 2
\]
This is **true**.
### For the second inequality:
Again substituting \( x = 0 \):
\[
3y > 3(0) - 6 \implies 3y > -6
\]
Now substitute \( y = -3 \):
\[
3(-3) > -6 \implies -9 > -6
\]
This is **false**.
### Conclusion:
Since the point \( (0, -3) \) satisfies the first inequality but does not satisfy the second inequality, it is not a viable solution for the system.
1. \( y < -5x + 2 \)
2. \( 3y > 3x - 6 \)
we will substitute \( x = 0 \) and \( y = -3 \) into each inequality separately.
### For the first inequality:
Substituting \( x = 0 \):
\[
y < -5(0) + 2 \implies y < 2
\]
Now substitute \( y = -3 \):
\[
-3 < 2
\]
This is **true**.
### For the second inequality:
Again substituting \( x = 0 \):
\[
3y > 3(0) - 6 \implies 3y > -6
\]
Now substitute \( y = -3 \):
\[
3(-3) > -6 \implies -9 > -6
\]
This is **false**.
### Conclusion:
Since the point \( (0, -3) \) satisfies the first inequality but does not satisfy the second inequality, it is not a viable solution for the system.