SOLUTION: A triangle has a perimeter of 197 cm. The sum of the smallest and medium sides is 49 more than the longest side. The difference between the longest and shortest sides is 22. Fin

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x = y+z-49
x = y+22
therefore y+22 = y+z-49 because x = y+z-49 = y+22
y+22 = y+z-49
y+22-y-22 = y+z-49-y-22
0 = z-71
0+71 = z-71+71
[z = 71] ( So now we know that z is 71 )
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x+y+z = 197 ( z = 71 )
x+y+71 = 197
x+y = 126
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x-y = 22 ( x-22=y so x-y=22 )
x+y = 126 ( use subtitution to slove for x )
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2x = 148
[x = 74]
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x+y+z = 197
74+y+71 = 197
[y = 52]
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So [x = 74] (the longest side)
[y = 52] (the shortest side)
[z = 71] (the medium side)