Chapter 9.1, Problem 74PE

The purchase price of a home $y$ (in $\text{\$}1000$ ) can be approximated based on the annual income of the buyer $x_1$ (in $\text{\$}1000$ ) and on the square footage of the home $x_2$ (in $100{\text{ ft}}^2$ ) according to $y=a{x}_1+b{x}_2+c.$

The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home.

a. Use the data to write a system of linear equations to solve for $a,b$ , and $c$ .

b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c. Write the model $y=a{x}_1+b{x}_2+c.$

d. Predict the purchase price for a buyer who makes $\text{\$}100,000$ per year and wants a $2500{\text{ ft}}^2$ home.