Fill in each blank so that the resulting statement is true.
The solution set of the system
left brace Start 2 By 3 Matrix 1st Row 1st Column x minus y 2nd Column less than 3rd Column 1 2nd Row 1st Column 4 x plus 5 y 2nd Column greater than or equals 3rd Column 14 EndMatrix x−y	<	1	4x+5y	≥	14 
is the set of ordered pairs that satisfy​ _____ and​ _____.
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Part 1
The solution set of the system
left brace Start 2 By 3 Matrix 1st Row 1st Column x minus y 2nd Column less than 3rd Column 1 2nd Row 1st Column 4 x plus 5 y 2nd Column greater than or equals 3rd Column 14 EndMatrix x−y	<	1	4x+5y	≥	14 
is the set of ordered pairs that satisfy 
▼ 
 and 
▼ 

To find the solution set for the system of inequalities:

1. **Inequality 1**: \( x - y < 1 \)  
2. **Inequality 2**: \( 4x + 5y \geq 14 \)

The solution set of the system is the set of ordered pairs \((x, y)\) that satisfy both inequalities.

Thus, we can fill in the blanks as follows:

The solution set of the system is the set of ordered pairs that satisfy **\( x - y < 1 \)** and **\( 4x + 5y \geq 14 \)**.

### Want More Help?
Would you like to see the graphical representation of these inequalities or further explore their implications? Here are some related questions:

1. What is the graphical representation of these inequalities?
2. How can we determine the boundary lines for each inequality?
3. What are some specific ordered pairs that satisfy both inequalities?
4. How do these inequalities define a feasible region?
5. What methods can be used to solve systems of inequalities?

**Tip**: Always graph inequalities to visualize the solution set and confirm where the regions overlap.

Fill in each blank so that the resulting statement is true. The solution set of the system is the set of ordered pairs that satisfy _____ and _____.

Explore how to solve the system of inequalities x - y < 1 and 4x + 5y ≥ 14. This guide provides a comprehensive overview of the inequalities involved, their graphical representations, and methods for determining the solution set. Ideal for high school students.

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