Respuesta :
Solving system of equations in two variable gives that the number of cards in every booster pack are 10 and number of cards in every premade deck are 32
What is system of equations in two variables and how to find its solution by substitution?
Let x and y be two variables and
a₁x+b₁y =c₁
a₂x+b₂y =c₂
Where a₁, a₂, b₁, b₂, c₁, c₂ are constants then we can solve these simultaneous equations by substitution take value of x from equation (1) and then put it in (2) to get an equation for y only and then solve for y. put value of y in equation (1) to get value of x.
Let the number of cards in every booster pack are x and the number of cards in every premade deck be y
Number of cards in 5 booster packs will be 5x and Number of cards in 4 premade deck will be 4y
As Oliver purchases 5 booster packs and 4 premade decks, which included a total of 178 cards.
Thus we get 5x + 4y = 178 .....(1)
Number of cards in 4 booster packs will be 4x and Number of cards in 7 premade deck will be 7y
As Oliver received 4 booster packs and 7 premade decks, which included a total of 178 cards.
Thus we get 4x +7y = 264 ...(2)
System of equations to be solved is
5x + 4y = 178 .....(1)
4x +7y = 264 ...(2)
From (1) , we get x = [tex]\frac{178-4y}{5}[/tex]
Put this value in (2)
[tex]4(\frac{178-4y}{5}) +7y= 264\\\frac{712}{5} -\frac{16y}{5} +7y = 264\\\frac{712}{5}-264=\frac{16y}{5} -7y\\ y= 32\\x= \frac{178-4(32)}{5 }\\ x=50/5\\x=10[/tex]
Therefore x=10 and y= 32
The number of cards in every booster pack are 10 and number of cards in every premade deck are 32
Learn more about the solution of system of linear equation in two variable at https://brainly.com/question/14495718
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