Answer:
See answers below
Step-by-step 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
