Answer
$6$ science exercises
$12$ math exercises
Work Step by Step
We are told that there are total of $18$ math and science exercises to do. If we let $m$ be the number of math exercises and $s$ be the number of science exercises, we can write an equation to represent the situation.
Total of $18$ math and science exercises $$18 = m + s.$$ We can rearrange this equation, so it will be easier to plot it later. $$m=-s+18.\tag{1}$$ We also know that there are $6$ more math exercises than science exercises. We will write another equation to represent this information. In order to write an equality sign we have to add $6$ to the side that represents science exercises: $$m=s+6.\tag{2}$$ We graph equations $(1)$ and $(2)$. From the graph, we can see that the solution, or point of intersection, to this system of equations is the point $(6,12)$, so $s=6$, $m=12$.
However, we should check the point by substituting it into the equations.
Let's start with the first one.
$$\begin{align}
m& =-s+18\\
12&\stackrel{?}{=} -6+18\\
12&=12\checkmark.
\end{align}$$ Now, we will check the second one.
$$\begin{align}
m& =s+6\\
12&\stackrel{?}{=} 6+6\\
12&=12\checkmark.
\end{align}$$ Since both equations hold true, the point $(6,12)$ is the solution. This means that we have $6$ science exercises and $12$ math exercises for homework.
