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bridgettegale95
Part 1: For the following system of equations, write your own real world scenario that describes what is happening. Use complete sentences and correct grammar in your scenario. Part 2: Solve the system and explain what the results mean according to your scenario. 2x + y = 11 3x + 4y = 24
2 lollipops and the bottle of cola cost 11 dollars. 3 lollipops and 4 bottles of cola cost 24 dollars
y=11-2x 3x+4(11-2x)=24 3x+44-8x=24 -5x=-20 x=4 y=11-8 y=3 lollipop costs 4dollars, cola 3 dollars
I have 11 DVD's in total I have got some DVD's from Tom and twice as many from Bob. How many DVD's did Tom and Bob give me? Or I have 24 DVD's in total I have got some DVD's from 3 times as much from Tom and four times as much from Bob. How many DVD's did Tom and Bob give me? With this example we can use the two variables for the two friends x = Bob y = Tom 2x + y = 11 3x + 4y = 24 to solve this we can use the process of elimination in order to use elimination we need to make one of the variables the same value on both equations through multiplication We can choose to get Y on its own and to do that we need to cancel out X so we do 2x + y = 11 (multiply by 3) 3x + 4y = 24 (multiply by 2) 6x + 3y = 33 6x + 8y = 48 Now we have the same value for x in both equations all we need to do is minues the two equations from eachother. So we get 5y = 15 we divide both sides by 5 in order to get Y by it self and making Y the subject With this we can solve what Y is 5y / 5 = 15 / 5 so we will get y = 3 now we know the value of Y we can use this value to work out X by using this value in any of the two formulas 2x + y = 11 3x + 4y = 24 we will choose to use the value in the first equation (although you can also choose to use it in the second if you want) so we will get 2x + 3 = 11 we need to rearrange this formula to get the variables on one side and numbers on the other (remember when bringing a number to the other side will change its value e.g. bringing 3 to the other side will give you -3) so we will get 2x = 11 - 3 2x = 8 now we divde both sides by 2 to get X on its own and making X the subject 2x / 2 = 8 / 2 so we will get x = 4 place these values in any of the equations to check the answer is correct I will use the second equation to check (although you can also use the first just to double check) so we know x = 4 and y = 3 the second equation is 3x + 4y = 24 so we will get 3(4) + 4(3) = 24 12 + 12 = 24 Hope you understand if not please do let us know and dont forget to click good answer :)