To determine the correct system of equations for the given problem, let's analyze the information provided:
1. The artist bought [tex]$x$[/tex] small paintbrushes and [tex]$y$[/tex] large paintbrushes.
2. The total number of paintbrushes is 10.
3. The number of small paintbrushes is 4 times the number of large paintbrushes.
We need to translate this information into mathematical equations.
First, the total number of paintbrushes:
[tex]\[ x + y = 10 \][/tex]
This equation indicates that the sum of small paintbrushes [tex]\(x\)[/tex] and large paintbrushes [tex]\(y\)[/tex] is 10.
Next, the relationship between the number of small and large paintbrushes:
[tex]\[ x = 4y \][/tex]
This equation tells us that the number of small paintbrushes [tex]\(x\)[/tex] is 4 times the number of large paintbrushes [tex]\(y\)[/tex].
Now, we have a system of equations:
[tex]\[
\begin{aligned}
x + y &= 10 \\
x &= 4y
\end{aligned}
\][/tex]
Thus, the system of equations that can be used to find the numbers of small paintbrushes and large paintbrushes in the set is:
(A)
[tex]\[
\begin{array}{l}
x + y = 10 \\
x = 4 y
\end{array}
\][/tex]
So, the correct choice is (A).
