At the theater, the Seward family bought 2 adult tickets and 3 children's tickets for $44.50. The Sena family bought 3 adult tickets and 6 children's tickets for $78. Find the price of an adult ticket and the price of a child's ticket.

Adult ticket is $7.5 while a child's ticket is $11

Step-by-step explanation:

Given data

Let the cost of an adult ticket be x

and the cost of a child ticket be y

The Seward family

2x+3y= 44.501

The Sena family

3x+6y= 782

solve 1 and 2

2x+3y= 44.50   X2

3x+6y= 78        X1

   4x+6y= 89

- 3x+6y= 78

  x+ 0= 11

x= 11

put x= 11 in 1

2x+3y= 44.50

2*11+3y= 44.5

22+3y=44.5

3y= 44.5-22

3y= 22.5

y= 22.5/3

y= 7.5

Hence Adult ticket is $7.5 while a child's ticket is $11

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!