Is (1, 4) a solution to this system of inequalities? 8x + y ≥ 6 3x + 2y < 18 Choices: (A)yes (B)no

Check Point (1, 4): Does the point (1, 4) satisfy the inequality 8x + y ≥ 6? Substitute 1 for x and 4 for y in 8x + y ≥ 6. 8(1) + 4 ≥ 6 8 + 4 ≥ 6 12 ≥ 6 Since 12 ≥ 6 is true, (1, 4) satisfies the inequality 8x + y ≥ 6.Check Inequality 1: Does the point (1, 4) satisfy the inequality 3x + 2y < 18? Substitute 1 for x and 4 for y in 3x + 2y < 18. 3(1) + 2(4) < 18 3 + 8 < 18 11 < 18 Since 11 < 18 is true, (1, 4) satisfies the inequality 3x + 2y < 18.Check Inequality 2: Is (1, 4) a solution to the system of inequalities? Since (1, 4) satisfies both inequalities: 12 ≥ 6 (true) 11 < 18 (true) Therefore, (1, 4) is a solution to the system of inequalities.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Is $(1,\ 4)$ a solution to this system of inequalities? $\newline$ $8x + y \geq 6$ $\newline$ 3x + 2y < 18 $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

View step-by-step help

Home

Math Problems

Algebra 1

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

Full solution

Q. Is

(1,\ 4)

a solution to this system of inequalities?

\newline

8x + y \geq 6

\newline

3x + 2y < 18

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $1, 4$ : Does the point $1, 4$ satisfy the inequality $8x + y \geq 6$ ? $\newline$ Substitute $1$ for $x$ and $4$ for $y$ in $8x + y \geq 6$ . $\newline$ $8(1) + 4 \geq 6$ $\newline$ $8 + 4 \geq 6$ $\newline$ $1, 4$ $0$ $\newline$ Since $1, 4$ $0$ is true, $1, 4$ satisfies the inequality $8x + y \geq 6$ .
Check Inequality $1$ : Does the point $(1, 4)$ satisfy the inequality 3x + 2y < 18? $\newline$ Substitute $1$ for $x$ and $4$ for $y$ in 3x + 2y < 18. $\newline$ 3(1) + 2(4) < 18 $\newline$ 3 + 8 < 18 $\newline$ 11 < 18 $\newline$ Since 11 < 18 is true, $(1, 4)$ satisfies the inequality 3x + 2y < 18.
Check Inequality $2$ : Is $(1, 4)$ a solution to the system of inequalities? $\newline$ Since $(1, 4)$ satisfies both inequalities: $\newline$ $12 \geq 6$ (true) $\newline$ 11 < 18 (true) $\newline$ Therefore, $(1, 4)$ is a solution to the system of inequalities.