Question

Identify any solutions to the system shown here.2x+3y 263x+2y ≤ 6(1.5, 1)(0.5, 2)(-1, 2.5)(-2,4)

Answer 1

Answer:

the solution to the system given is (0.5, 2) (2nd option)

Step-by-step explanation:
`\begin{gathered} 2x+3y\ \ge6 \\ 3x+2y\le6 \end{gathered}`

To find:

the solution the system given

To determine this, we will check each of the given points:

`\begin{gathered} a)\text{ }Point\text{ \lparen1.5, 1\rparen} \\ 2(1.5)+3(1)\ge6\text{ } \\ 6\ge6\text{ \lparen correct\rparen} \\ 3(1.5)+2(1)\le6 \\ 6.5\le6\text{ \lparen wrong\rparen} \\ \\ b)\text{ Point \lparen0.5, 2\rparen} \\ 2(0.5)+3(2)\ge6\text{ } \\ 7\ge6\text{ \lparen correct\rparen} \\ 3(0.5)+2(2)\le6 \\ 5.5\le6\text{ \lparen correct\rparen} \end{gathered}`
`\begin{gathered} c)\text{ \lparen-1, 2.5\rparen} \\ 2(-1)+3(2.5)\ge6 \\ 5.5\ge6\text{ \lparen wrong\rparen} \\ 3(-1)+2(2.5)\le6 \\ 2\text{ }\le6\text{ \lparen correct\rparen} \\ \\ d)\text{ \lparen-2, 4\rparen} \\ 2(-2)+3(4)\ge6 \\ 3\ge6\text{ \lparen wrong\rparen} \\ 3(-2)+2(4)\le6 \\ 2\le6\text{ \lparen correct\rparen} \\ \end{gathered}`

Only the point (0,5, 2) have both inequality statements correct. Hence, the solution to the sytem given is (0.5, 2) (2nd option)