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Math 114N Week 5 Discussion: Systems of Equations in the Real WorldInitial Post InstructionsIf you have a problem that has multiple variables, you can solve it using a system of equations. Think of a real-world example where you would need to solve using a system of equations. Write two or three sentences describing your example. Include the equations in your description, but do not solve the system. That will be left to your classmates.For this week's discussion we are going over system of equations. My example of such isMy sister and I decided to go to Mcdonalds for dinner. I ordered 3 hot and spicy sandwiches and 3 medium fry that totaled to $11.25. My sisters total for 4 hot and spicy sandwiches and 2 medium fry was $10. How much do the hot and spicy sandwiches and medium fry cost independently. Our variables will be:x= cost of a hot and spicy y= cost of a medium frySo for my dinner in equation form:3 hot and spicys and 3 medium fry will cost= $11.25 3x+3y=11.25My sisters order in equation form:4 hot and spicys and 2 medium fry=$10 4x+2y=10
Now to find the price of each item I need to rewrite the equation with opposite teams to find the x value. So:2[3x+3y=11.25]2[3x+3y=11.25]6x+6y=22.506x+6y=22.50and −3[4x+2y=10]−3[4x+2y=10]−12x−6y=−30−12x−6y=−30now we will combine −12x−6y=−30−12x−6y=−306x+6y=22.506x+6y=22.50−6x=−7.50−6x=−7.50−6=−6−6=−6x=1.25x=1.25Now to find y4x+2y=104x+2y=104(1.25)+2y=104(1.25)+2y=105+2y=105+2y=10
5−5+2y=10−55−5+2y=10−5(subtract by 5 on both sides)2y=52y=5(divide by 2)y=2.5y=2.5So one hot and spicy will cost $1.25 and one medium fry will cost $2.50