Is (–8,1) a solution to this system of inequalities?
y>6x+10
y≥–x–7
To check if (-8, 1) is a solution to the system of inequalities, we substitute x = -8 and y = 1 into the inequalities:
1. y > 6x + 10
1 > 6(-8) + 10
1 > -48 + 10
1 > -38
This is true, so the point (-8, 1) satisfies the first inequality.
2. y ≥ -x - 7
1 ≥ -(-8) - 7
1 ≥ 8 - 7
1 ≥ 1
This is also true, so the point (-8, 1) satisfies the second inequality.
Therefore, the point (-8, 1) is a solution to the system of inequalities.