Explanations;
Let the number of pots be "x"
Let the number of buckets be "y"
Since we have 192 items, hence;
x + y = 192 ............................... 1
If Pitts bought pots for 5 dollars each and joe bought buckets for 7dollars each and spent 140 dollars, this can be expressed as:
5x + 7y = 140 ............................ 2
Solve the equations simultaneously to get the value of x and y:
x + y = 192 ............................... 1 * 7
5x + 7y = 140 ............................ 2 * 1
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7x + 7y = 1344
5x + 7y = 140
Subtract
7x - 5x = 1344 - 140
2x = 1204
x = 1204/2
x = 602
This shows that 602 pots were bought.
Substitute x = 602 into the equation 1 to get y:
602 + y = 192
y = 192 - 602
y = -410
Since the y value cannot be negative, we can say that 602 pots were bought but the solution to the system of equation is (602, -410)