Algebra I, Systems of Linear Equations

Question

The pep club and honor society are joining forces to raise money for school improvements. Together they hope to raise at least $500. The pep club is holding a raffle that will raise at least $100. The system of inequalities representing this situation is:

x+y ≥ 500

x ≥ 100

where x represents pep club donations and y represents donations raised by the honor society.

(A) Graph this system of equalities.

(B) What does the point (300, 100) represent? Is it a viable solution? Why or why not?

(C) What does the point (500, 200) represent? Is it a viable solution? Why or why not?

THANK YOU

Answer 1

(A) x+y >=500

y >= 500 - x

= -x + 500

the slope is -1; the intercept is 500.

So (0,500) is a point on this line, namely the y-intercept.

THe x-intercept is 0 = -x+500

-500 = -x

x = 500

So (500,0) is the x-intercept.

Connect (0,500) and (500,0) with a SOLID line since the inequality has EQUALS in it

The origin (0,0) is NOT a solution for this inequality so shade ABOVE this line

X>=100 is a vertical solid line at x=100, shading to the RIGHT.

THe solution shall be ABOVE the first line but to the right of the vertical line.

You can go to desmos dot com and graph it there to get a better picture

(B) (300,100) means the pep club raises 300 and the honors club raises 100.

Unfortunately this is not a solution of the inequality, as 300+100 = 400 < 500

which means they did NOT raise the funds to meet the goal

(C) (500,200) on the other hand is a viable solution, as the pep club raised 500 and

the honors club raised 200 for a total of 700 . the pep club met the goal singlehandedly