Is (3, 7) a solution to this system of inequalities? x + 12y ≤ 10 18x + 5y ≥ 7
To check if (3, 7) is a solution to the system of inequalities, we substitute the values of x and y into each inequality and see if the inequality holds true.
1st inequality: x + 12y ≤ 10
Substituting x = 3 and y = 7:
3 + 12(7) ≤ 10
3 + 84 ≤ 10
87 ≤ 10
The inequality 87 ≤ 10 is not true, so (3, 7) is not a solution to the first inequality.
2nd inequality: 18x + 5y ≥ 7
Substituting x = 3 and y = 7:
18(3) + 5(7) ≥ 7
54 + 35 ≥ 7
89 ≥ 7
The inequality 89 ≥ 7 is true, so (3, 7) is a solution to the second inequality.
Since (3, 7) is not a solution to both inequalities in the system, it is not a solution to the system of inequalities.