Which ordered pair is a solution to the system of inequalities shown on the graph?

Mathematics

1 answer:

wolverine [178]3 years ago

7 0

Answer:

5,2

Step-by-step explanation:

Here, we want to find the point that is a solution to the system of inequalities

From what we have, the points that lie in the dark brown patch represent the solution to the system

Hence the coordinates lying in these parts are the solution to the system

An example of such coordinates is the point (5,2)

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$\left\{\begin{array}{ccc}2x+3y=134\\x+5y=179&|\text{subtract 5y from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+3y=134\\x=179-5y&|\text{substitute to the first equation}\end{array}\right\\\\2(179-5y)+3y=134\qquad\text{use distributive property}\\\\(2)(179)+(2)(-5y)+3y=134\\\\358-10y+3y=134\qquad\text{subtract 358 from both sides}\\\\-7y=-224\qquad\text{divide both sides by (-7)}\\\\\boxed{y=32}\\\\\text{Put the value of y to the second equation}\\\\x=179-5(32)\\\\x=179-160\\\\\boxed{x=19}$

<h3>Answer: video tape cost $19 and DVD cost $32.</h3>