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The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

Let the number of bottles of paint bought be x and the number of paint brushes bought be y.

As per the conditions the system of equations thus formed will be:

$x+y=10$ … (1)

$5x+1.50y=36$ … (2)

Multiply equation (1) by 5.

$$\begin{gathered} 5\left(x+y\right)=5×\left(10\right) \\ 5x+5y=50\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}\left(3\right) \end{gathered}$$

Note that both the equations (2) and (3) have $5x$in same sign, therefore, variable $x$can be eliminated if both equations are subtracted.

$\begin{array}{l}\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}5x+5y=50\\ \underset{¯}{\left(−\right)\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}5x+1.50y=36}\\ \text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â€‰â€‰â€‰â€‰â€‰}3.5y=14\text{Dividebothsidesby3.5}\\ \text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â€‰â€‰â€‰â€‰}y=4\end{array}$

Substitute 4 for y into the equation (1) and solve for x.

$\begin{array}{c}x+y=10\\ x+\left(4\right)−4=10−4\\ x=6\end{array}$

Therefore, the number of bottles of paint and the number of paint brushes bought are 6 and 4 respectively.