((-1,5); (0.923, 1.6) 5 10 -5 o(- 4s - 2) Which of the points on the graph is a solution for the simultaneous inequalities y > 4x - 2 and y >= - 1/3 * x + 2' Enter the x-value followed by the y -value .
To determine which points on the graph satisfy the simultaneous inequalities, we can substitute the x-values and y-values of each given point into the inequalities and check if they hold true.
For the first inequality, y > 4x - 2:
- For the point (-1, 5):
Substitute x = -1 and y = 5 into the inequality,
5 > 4(-1) - 2
5 > -4 - 2
5 > -6
This inequality holds true.
- For the point (0.923, 1.6):
Substitute x = 0.923 and y = 1.6 into the inequality,
1.6 > 4(0.923) - 2
1.6 > 3.692 - 2
1.6 > 1.692
This inequality holds true.
For the second inequality, y >= - 1/3 * x + 2:
- For the point (-1, 5):
Substitute x = -1 and y = 5 into the inequality,
5 >= -1/3 * (-1) + 2
5 >= 1/3 + 2
5 >= 2.333
This inequality holds true.
- For the point (0.923, 1.6):
Substitute x = 0.923 and y = 1.6 into the inequality,
1.6 >= -1/3 * (0.923) + 2
1.6 >= -0.3077 + 2
1.6 >= 1.6923
This inequality does not hold true.
Therefore, the solution point for the simultaneous inequalities is (-1, 5).
Are you sure
Apologies for the error in my previous response. Let's recheck the solution.
For the first inequality, y > 4x - 2:
- For the point (-1, 5):
Substitute x = -1 and y = 5 into the inequality,
5 > 4(-1) - 2
5 > -4 - 2
5 > -6
This inequality holds true.
- For the point (0.923, 1.6):
Substitute x = 0.923 and y = 1.6 into the inequality,
1.6 > 4(0.923) - 2
1.6 > 3.692 - 2
1.6 > 1.692
This inequality does not hold true.
For the second inequality, y >= -1/3 * x + 2:
- For the point (-1, 5):
Substitute x = -1 and y = 5 into the inequality,
5 >= -1/3 * (-1) + 2
5 >= 1/3 + 2
5 >= 2.333
This inequality holds true.
- For the point (0.923, 1.6):
Substitute x = 0.923 and y = 1.6 into the inequality,
1.6 >= -1/3 * (0.923) + 2
1.6 >= -0.3077 + 2
1.6 >= 1.6923
This inequality does not hold true.
Therefore, after rechecking the solution, we find that the only point satisfying the simultaneous inequalities is (-1, 5).