Question

Which point is a solution to the inequality2x - 3y ≥ 12

Answer 1

Given:

$2x-3y\ge12$

Add 3y-12 to both sides of the inequality, we get

$2x-3y+3y-12\ge12+3y-12$

$2x-12\ge3y$

Dividing both sides by 3, we get

$\frac{2x-12}{3}\ge\frac{3y}{3}$

$\frac{2x-12}{3}\ge y$

Let x=9 and substitute in this inequality, we get

$\frac{2(9)-12}{3}\ge y$

$\frac{18-12}{3}\ge y$

$\frac{6}{3}\ge y$

$2\ge y$

We get 2 is greater than or equal to y.

y values are 2,1,0,...

Hence the solutions to the given inequality are

$(9,2),(9,1),(9,0)$

We need to check all the given options.

$(4,2)$

Substitute x=4 and y=2 in the inequality, we get

$2(4)-3(2)\ge12$

$2\ge12$

This is not true.

$(2,5)$

Substitute x=2 and y=5 in the inequality, we get

$2(2)-3(5)\ge12$

$-11\ge12$

This is not true.

$(1,1)$

Substitute x=1 and y=1 in the inequality, we get

$2(1)-3(1)\ge12$

$-1\ge12$

Hence the solution is

$(9,2)$