Question

1. $yleq -1$ $2x - y > 3$ 8) $x + y < -1$ $x + y < -3$ 9) $x - y < 3$ $2x + y > 3$ 10) $4x - 3y geq 6$ $x + 3y geq 9$

Explanation:

Problem 7

Step1: Rewrite 2nd inequality for y

$2x - y > 3 \implies y < 2x - 3$

Step2: Combine with 1st inequality

Final system: $y \leq -1$ and $y < 2x - 3$

Problem 8

Step1: Analyze overlapping inequalities

$x+y < -3$ is stricter than $x+y < -1$, so only the stricter one applies.

Problem 9

Step1: No simplification needed

System remains: $x - y < 3$ and $2x + y > 3$

Problem 10

Step1: No simplification needed

System remains: $4x - 3y \geq 6$ and $x + 3y \geq 9$

Answer:

1. The simplified system is $\boldsymbol{y \leq -1}$ and $\boldsymbol{y < 2x - 3}$
2. The simplified system is $\boldsymbol{x+y < -3}$
3. The system remains $\boldsymbol{x - y < 3}$ and $\boldsymbol{2x + y > 3}$
4. The system remains $\boldsymbol{4x - 3y \geq 6}$ and $\boldsymbol{x + 3y \geq 9}$