Question

select all of the points that satisfy the inequality $-2x + 3y \geq 10$.\
$\square$ $(1,6)$\
$\square$ $(3,5)$\
$\square$ $(-2,2)$\
$\square$ $(-7,-2)$

Explanation:

Step1: Substitute (1,6)

Substitute \(x = 1\), \(y = 6\) into \(-2x + 3y\):
\(-2(1)+3(6)=-2 + 18 = 16\)
Since \(16\geq10\), (1,6) satisfies the inequality.

Step2: Substitute (3,5)

Substitute \(x = 3\), \(y = 5\) into \(-2x + 3y\):
\(-2(3)+3(5)=-6 + 15 = 9\)
Since \(9<10\), (3,5) does not satisfy the inequality.

Step3: Substitute (-2,2)

Substitute \(x=-2\), \(y = 2\) into \(-2x + 3y\):
\(-2(-2)+3(2)=4 + 6 = 10\)
Since \(10\geq10\), (-2,2) satisfies the inequality.

Step4: Substitute (-7,-2)

Substitute \(x=-7\), \(y=-2\) into \(-2x + 3y\):
\(-2(-7)+3(-2)=14-6 = 8\)
Since \(8<10\), (-7,-2) does not satisfy the inequality.

Answer:

(1,6), (-2,2)