A detector calibration line should map several unknown signals, not just one. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The line maps the first unknown
Standards 1 and 11 fix slope 2. The first signal 6 maps to value 3.
x=6/2=3
The middle unknown uses the same slope
signal 14 maps to value 7. Same standards, same inverse line.
x=14/2=7
The high unknown stays inside the range
signal 20 maps to value 10. Three rows make the calibration relation visible, not guessed.