a The system of inequalities for this exercise will have two inequalities. One will represent cost and the other will represent the number of pounds. For both we will let

x

represent the number of pounds of blueberries purchased and

y

represent the number of pounds of strawberries purchased.

Inequality I: It is given that one pound of blueberries costs $4$ dollars, one pound of strawberries costs $3$ dollars, and we can spend at most $21$ dollars. The phrase at most is represented by the symbol $\leq .$ Let's write this inequality.

4 x + 3 y \leq 21

Inequality II: It is given that we need at least $3$ pounds of fruit. The phrase at least is represented by $\geq .$ Now, let's write the second inequality.

x + y \geq 3

With these two inequalities, we can represent this situation as a system.

{4 x + 3 y \leq 21 x + y \geq 3 (I) (II)

Writing in Slope-Intercept Form

To graph the system, it is helpful if we rewrite the inequalities in slope-intercept form. For Inequality (II) this only requires subtracting

x

from both sides.

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