<u><em>Answer:</em></u>
Number of adult tickets = 3 tickets
Number of children tickets = 5 tickets
<u><em>Step-by-step explanation:</em></u>
<u>A- The system of equations:</u>
Assume that the number of adult tickets is x and that the number of children tickets is y
<u>We are given that:</u>
i. The total number of people in the group is 8, which means that the total number of tickets bought is 8. <u>This means that:</u>
x + y = 8 ..................> equation I
ii. The price of an adult ticket is $12 and that of a child ticket is $10. We know that the group spent a total of $86. <u>This means that:</u>
12x + 10y = 86 ...............> equation II
<u>From the above, the systems of equation is:</u>
x + y = 8
12x + 10y = 86
<u>B- Solving the system using elimination method:</u>
Start by multiplying equation I by -10
<u>This gives us:</u>
-10x - 10y = -80 .................> equation III
Now, taking a look at <u>equations II and III</u>, we can note that coefficients of the y have equal values and different signs.
<u>Therefore, we will add equations II and III to eliminate the y</u>
12x + 10y = 86
+( -10x - 10y = -80)
<u>Adding the two equations, we get:</u>
2x = 6
x = 3
<u>Finally, substitute with x in equation I to get the value of y:</u>
x + y = 8
3 + y = 8
y = 8 - 3 = 5
<u>Based on the above:</u>
Number of adult tickets = x = 3 tickets
Number of children tickets = y = 5 tickets
<u>C- Explanation of the meaning of the solution:</u>
The above solution means that for a group of 8 people to be able to spend $86 in a theater having the price of $12 for an adult ticket and $10 for a child' one, this group must be composed of 3 adults and 5 children
Hope this helps :)