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 x_2 (text{ in } 100ft^2) according to y=ax_1+bx_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=ax_1+bx_2+c d) Predict the purchase price for a buyer who makes $100000 per year and wants a 2500ft^2 home.

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 x_2 (text{ in } 100ft^2) according to y=ax_1+bx_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=ax_1+bx_2+c d) Predict the purchase price for a buyer who makes $100000 per year and wants a 2500ft^2 home.

Question
Forms of linear equations
asked 2020-10-19
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 \(x_2 (\text{ in } 100ft^2)\) according to \(y=ax_1+bx_2+c\)
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 \(y=ax_1+bx_2+c\)
d) Predict the purchase price for a buyer who makes $100000 per year and wants a \(2500ft^2\) home.

Answers (1)

2020-10-20
\(y=ax_1+bx_2+c\)
We have to determine the function:
\(\begin{cases}80a+21b+c=180\\ 150a+28b+c=250\\ 75a+18b+c=160 \end{cases}\) Set up a system of equations for a,b,c:
\(\begin{bmatrix}80&21&1&|&180\\150&28&1&|&250\\75&18&1&|&160\end{bmatrix}\)
b) Build the augmented matrix:
\(\begin{bmatrix}1&0&0&|&0.4\\0&1&0&|&6\\0&0&1&|&22\end{bmatrix}\)
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:
\(y=0.4x_1+6x_2+22\)
write the model y that fits the data:
\(y=0.4(100)+6(25)+22=212\)
d) Determine y for \(x_1=100 , x_2=25\)
0

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1
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