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ax+3y >= 7

2y <= ax+2
In the system of inequalities,
a is a constant. If
(1,2) is a solution to the system, which of the following is a possible value of
a ?
Choose 1 answer:
(A) -2
(B) -1
(C) 1
(D) 2

$a x+3 y \geq 7$ $\newline$ $2 y \leq a x+2$ $\newline$ In the system of inequalities, $a$ is a constant. If $(1,2)$ is a solution to the system, which of the following is a possible value of $a$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-2$ $\newline$ (B) $-1$ $\newline$ (C) $1$ $\newline$ (D) $2$

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Is (x, y) a solution to the system of linear inequalities?

Full solution

Q.

a x+3 y \geq 7

\newline

2 y \leq a x+2

\newline

In the system of inequalities,

a

is a constant. If

(1,2)

is a solution to the system, which of the following is a possible value of

a

?

\newline

Choose

1

answer:

\newline

(A)

-2

\newline

(B)

-1

\newline

(C)

1

\newline

(D)

2

Substitute Point $(1,2)$ : Substitute the point $(1,2)$ into the first inequality $ax+3y \geq 7$ . $\newline$ Calculation: $a(1) + 3(2) \geq 7$ $\newline$ $a + 6 \geq 7$ $\newline$ $a \geq 7 - 6$ $\newline$ $a \geq 1$
Calculate First Inequality: Substitute the point $(1,2)$ into the second inequality $2y \leq ax+2$ . $\newline$ Calculation: $2(2) \leq a(1) + 2$ $\newline$ $4 \leq a + 2$ $\newline$ $a \geq 4 - 2$ $\newline$ $a \geq 2$
Calculate Second Inequality: Combine the results from both inequalities to find the possible values of $a$ . From the first inequality, we have $a \geq 1$ . From the second inequality, we have $a \geq 2$ . Therefore, $a$ must be greater than or equal to $2$ .

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