Answer
We bought $2$ small notebooks and $4$ large notebooks.
Work Step by Step
We need to set up a system of equations to find the solution.
First, we need to define two variables:
$x$ = the number of small notebooks we purchase
$y$ = the number of large notebooks we purchase
The number of books purchased is $6$ so $x + y = 6$.
Small notebooks are $8$ dollars each whereas the large notebooks are $10$ dollars apiece.
The total cost of the $6$ books is $\$56$.
Thus, $8x + 10y = 56$
Let us put the two equations together to solve for $x$ and $y$:
$x + y = 6$
$8x + 10y = 56$
Let's multiply the first equation by $8$ so that the $x$ terms for both equations can cancel each other out, leaving only the $y$ term:
$8x + 8y = 48$
$8x + 10y = 56$
We subtract the second equation from the first equation:
$(8x+8y)-(8x+10y)=48-56\\
-2y = - 8\\
y = \frac{8}{2}\\
y=4$
We can now use the value for $y$ to substitute into the first equation ($x + y = 6$) to find the value for $x$:
$x + 4 = 6\\
x=6-4\\
x=2$
We now know that we bought $2$ small notebooks and $4$ large notebooks.
