Exercise 2 Page 256

To determine if an ordered pair satisfies an equation, we substitute the point into the equation and simplify. If the resulting statement is true, then the point is contained in the solution set. For systems of inequalities, we can use the same method. However, substituting the point must create true statements in every inequality in the system. Let's test the given point.

y≥ 3x+1 & (I) y>x-1 & (II)

SubstituteII

x= 1, y= 4

4 ? ≥ 3( 1) + 1 4? >( 1)-1

Multiply

(I):Multiply

4 ? ≥3+1 4? >1-1

(I), (II):Add and subtract terms

4 ≥4 ✓ 4>0 ✓

Since 4 is greater than or equal to 4 and greater than 0, both statements are true. Therefore, the point (1,4) is contained in the solution set of the system.