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.

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