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Sagot :
Since there are two types of notebooks the sum of the number of each type should be equal to the total of notebooks bought, therefore:
[tex]x+y=7[/tex]x+y=7
Where "x" represents the number of spiral notebooks and "y" represents the number of three-ring notebooks.
If we multiply the number of each nobtebooks by their respective cost we should get the total value of the purchase, which is done below:
[tex]2.25\cdot x+6\cdot y=27[/tex]2.25x+6y=27
The system of equations is:
[tex]\mleft\{\begin{aligned}x+y=7 \\ 2.25\cdot x+6\cdot y=27\end{aligned}\mright.[/tex]x+y=7
2.25x+6y=27
To solve this system of equations we need to eliminate one variable. To do that we will multiply the first equation by -2.25
-2.25x-2.25y=-15.75
2.25x+6y=27
Now we will sum both equations as shown below:
-2.25x+2.25x-2.25y+6y=-15.75+27
3.75y=11.25
y=11.25/3.75=3
The value of y is 3, if we use it on the first equation we can find the value of x. We have:
x+3=7
x=7-3=4
With this we've solved the system. The purchase was 4 spiral notebooks and 3 three-ring ones.
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