Math Problem Statement

Is (5,-4) a solution to this system of inequalities? 17x+17y<18 and 15x+14y>20 yes or no

Solution

To determine whether (5,4)(5, -4) is a solution to the system of inequalities:

  1. First inequality: 17x+17y<1817x + 17y < 18

    • Substitute x=5x = 5 and y=4y = -4: 17(5)+17(4)=8568=1717(5) + 17(-4) = 85 - 68 = 17 Since 17<1817 < 18, the point satisfies the first inequality.
  2. Second inequality: 15x+14y>2015x + 14y > 20

    • Substitute x=5x = 5 and y=4y = -4: 15(5)+14(4)=7556=1915(5) + 14(-4) = 75 - 56 = 19 Since 192019 \not> 20, the point does not satisfy the second inequality.

Thus, the point (5,4)(5, -4) is not a solution to the system of inequalities.

Would you like more details on the reasoning? Here are 5 related questions:

  1. How do you determine if a point satisfies a system of inequalities?
  2. Can systems of inequalities have more than one solution?
  3. What happens when a point satisfies only one inequality in a system?
  4. How do graphical methods help in solving systems of inequalities?
  5. Can you solve systems of inequalities algebraically like systems of equations?

Tip: Always substitute each variable into the inequalities to check if both conditions hold.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Inequalities
Substitution Method

Formulas

Inequality: 17x + 17y < 18
Inequality: 15x + 14y > 20

Theorems

None (basic algebraic principles are applied)

Suitable Grade Level

Grades 9-10