Answer: the empty basket's mass is 0.28 kg
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Work Shown:
A = mass, in kg, of 1 apple
B = mass, in kg, of 1 empty basket
10A = mass of 10 apples
10A+B = mass of 10 apples and basket = 0.5
35A = mass of 35 apples
35A + B = mass of 35 apples and basket = 1.05
The system of equations we have is
There are a number of ways to solve. As the top left corner of your paper indicates, we can use a matrix to solve. Either using row reduction or matrix inverse math.
We could also use elimination which I find easiest in this case. I'll use that method. Subtract the equations straight down. Note how the B terms become B-B = 0B = 0 which go away. The A terms become 10A-35A = -25A, and the terms on the right hand side become 0.5-1.05 = -0.55
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We're left with the equation
-25A = -0.55
Divide both sides by -25 to isolate A
A = -0.55/(-25)
A = 0.022
The mass of one apple is 0.022 kg
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Use this value of A to find B
10A + B = 0.5
10*0.022 + B = 0.5
0.22 + B = 0.5
B = 0.5 - 0.22
B = 0.28
Or we could use the other equation to solve for B
35A + B = 1.05
35(0.022) + B = 1.05
0.77 + B = 1.05
B = 1.05 - 0.77
B = 0.28
Either way, the empty basket's mass is 0.28 kg