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The following three lines do not have a common intersection: x + y = 5, x - y = 4 and x + 2y = 4. However, we can find an "approximate solution" to this system of equations by finding a point (x, y) that is in some sense as close as possible to all three lines, simultaneously. ९ Find the coordinates of the point that minimizes the sum of the squares of the distances to each line, d² +d² + d². Hint: The distance of a point (x, y) to a line ax + by - c = 0 is given by Please show exact answers as whole numbers, decimals or fractions. |ax + by - c √a² + b²

The following three lines do not have a common intersection: x + y = 5, x - y = 4 and x + 2y = 4. However, we can find an "approximate solution" to this system of equations by finding a point (x, y) that is in some sense as close as possible to all three lines, simultaneously. ९ Find the coordinates of the point that minimizes the sum of the squares of the distances to each line, d² +d² + d². Hint: The distance of a point (x, y) to a line ax + by - c = 0 is given by Please show exact answers as whole numbers, decimals or fractions. |ax + by - c √a² + b²

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 101E
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The following three lines do not have a common intersection: x + y = 5, x - y = 4 and x + 2y = 4. However, we can find an "approximate solution" to this system of equations by finding a point (x, y) that is in some sense as close as possible to all three lines, simultaneously. ९ Find the coordinates of the point that minimizes the sum of the squares of the distances to each line, d² +d² + d². Hint: The distance of a point (x, y) to a line ax + by - c = 0 is given by Please show exact answers as whole numbers, decimals or fractions. |ax + by - c √a² +6²
Transcribed Image Text:The following three lines do not have a common intersection: x + y = 5, x - y = 4 and x + 2y = 4. However, we can find an "approximate solution" to this system of equations by finding a point (x, y) that is in some sense as close as possible to all three lines, simultaneously. ९ Find the coordinates of the point that minimizes the sum of the squares of the distances to each line, d² +d² + d². Hint: The distance of a point (x, y) to a line ax + by - c = 0 is given by Please show exact answers as whole numbers, decimals or fractions. |ax + by - c √a² +6²
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