Question

-2x + 2y = 2 4x –4y= 4A.No solutionB.One solution: x = _____ y = ___C.Infinitely many solutionsBONUS: A customer at a concession stand bought 2 boxes of popcorn and 3 drinks for $12. Another customerbought 3 boxes of popcorn and 5 drinks for $19. How much does a box of popcorn cost? _____________How much does a drink cost?__________________

Answer 1

See answers below

Explanation:

1) Given the simultaneous equation;

-2x + 2y = 2 .... 1 * 2

4x –4y= 4...2 * 1

____________

-4x + 4y = 4 .... 1

4x –4y= 4...2

Add both equations

4y-4y = 4-4

0y = 0

y = 0/0

Let x = k

Substitute x = k into 1

From 1: -2x + 2y = 2

-x+y = 1

-k + y = 1

y = 1+k

Hence the solution to the system of equation (x, y) is (k, 1 + k) where k is any integer.

The presence of k shows that the equation has many solutions since k can take any value

2) Let a box of popcorn be x

Let the cost of a drink be y

If a customer at a concession stand bought 2 boxes of popcorn and 3 drinks for $12, then;

2x + 3y = 12 ... 1

Also, if another customer bought 3 boxes of popcorn and 5 drinks for $19, then;

3x + 5y = 19 ...2

Solve 1 and 2 simultaneously

2x + 3y = 12 ... 1 * 3

3x + 5y = 19 ...2 * 2

_________________

6x + 9y = 36

6x + 10y = 38

Subtract

9y - 10y = 36 - 38

-y = -2

y = 2

Recall that 2x + 3y = 12

2x + 3(2) = 12

2x + 6 = 12

2x = 12-6

2x = 6

x = 6/2

x= 3

Hence a box of popcorn cost $3 and a drink cost $2