The amount of​ plate-glass sales S​ (in millions of​ dollars) can be affected by the number of new building contracts B issued​ (in millions) and automobiles A produced​ (in millions). A​ plate-glass company in a city wants to forecast future sales by using the past three years of sales. The totals for the three years are given in the table to the right. To describe the relationship among these​ variables, we can use the equation S=a+bA+cB, where the coefficients​ a, b, and c are constants that must be determined before the equation can be used. Complete parts ​(a) through​ (d). (a)Substitute the values for​ S, A, and B for each year from the table into the equation S=a+bA+cB​, and obtain three linear equations involving​ a, b, and c. Choose the correct answer below.

(b)Use a graphing calculator to solve this linear system for​ a, b, and c. Use matrix
inverse methods.

(c)Write the equation for S using these values for the coefficients.

(d)For the next year it is estimated that A=7.971 and B=47.39 Predict S.​ (The actual value for S was​ 865.6.)