Four Records, One Missing Reading

A team fits a small linear model with a bias term

$\hat{y} = b + w_1x_1 + w_2x_2 + w_3x_3$

to four calibration records. The model is required to reproduce all four recorded outputs exactly — four equations in the four unknowns $b, w_1, w_2, w_3$ , and the fit is unique.

Record	$x_1$	$x_2$	$x_3$	$y$
$1$	$1$	$2$	$4$	$5$
$2$	$2$	$1$	$6$	$11$
$3$	$3$	$4$	$2$	$6$
$4$	$0$	$3$	$8$	$2$

A fifth record then arrives with $x_2 = 7$ and $x_3 = 8$ , but its $x_1$ reading was corrupted and lost. The team does know that the fitted model outputs exactly $\hat{y} = 20$ for this record.

What was the missing $x_1$ reading?

Give your answer in units, rounded to two decimal places.

Four Records, One Missing Reading

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