# The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x_1 (in$1000) and on the square footage of the

The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer ${x}_{1}$ (in$1000) and on the square footage of the home 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 \$100000 per year and wants a $2500f{t}^{2}$ home.
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saiyansruleA
$y=a{x}_{1}+b{x}_{2}+c$
We have to determine the function:
$\left\{\begin{array}{l}80a+21b+c=180\\ 150a+28b+c=250\\ 75a+18b+c=160\end{array}$ Set up a system of equations for a,b,c:
$\left[\begin{array}{ccccc}80& 21& 1& |& 180\\ 150& 28& 1& |& 250\\ 75& 18& 1& |& 160\end{array}\right]$
b) Build the augmented matrix:
$\left[\begin{array}{ccccc}1& 0& 0& |& 0.4\\ 0& 1& 0& |& 6\\ 0& 0& 1& |& 22\end{array}\right]$
Use a graphing utility to find the reduced row-echelon form of the augmented matrix: $a=0.4,b=6,c=22$
c) Determine a,b,c:
$y=0.4{x}_{1}+6{x}_{2}+22$
write the model y that fits the data:
$y=0.4\left(100\right)+6\left(25\right)+22=212$
d) Determine y for ${x}_{1}=100,{x}_{2}=25$