document.write( "Question 174551This question is from textbook Algebra 2, Texas Edition
\n" ); document.write( ": As a participant in your school's community service project, you volunteer a total of 40 hours over the course of the school year. Your volunteer hours include serving at a soup kitchen, picking up trash at several local parks, and collecting toys for needy children. You spend 4 times as many hours collecting toys as picking up trash, and 2 hours less serving at the soup kitchen than picking up trash.
\n" ); document.write( "1. Solve this system of equations using Cramer's Rule. \n" ); document.write( "
Algebra.Com's Answer #129625 by Mathtut(3670)\"\" \"About 
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1. Write a system of equations to represent the given information and solve using the substitution method.
\n" ); document.write( "Please help and try to show every bit of work that you can to help me better understand the problem, Thank You! =)
\n" ); document.write( ":
\n" ); document.write( "lets call the time spent at soup kitchen,trash pickup, and toy collecting
\n" ); document.write( "s, t, and c, respectively
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\n" ); document.write( "c=4t...........eq 1
\n" ); document.write( "s=t-2..........eq 2
\n" ); document.write( "s+t+c=40.......eq 3
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\n" ); document.write( "rewrite equations
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\n" ); document.write( " s+t+c=40......eq 3
\n" ); document.write( " s-t+0c=-2.....eq 2
\n" ); document.write( "0s-4t+c=0......eq 1
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\n" ); document.write( "now writing out the main matrix
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\n" ); document.write( "\"%28matrix%283%2C3%2C1%2C1%2C1%2C1%2C-1%2C0%2C0%2C-4%2C1%29%29\"...lets call this matrix X
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\n" ); document.write( "we need to find the determinant of this matrix to begin with
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\n" ); document.write( "we can choose any row or column to determine this ..I will work with column 1 since it has a zero in it
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\n" ); document.write( "det X=(1) det\"%28matrix%282%2C2%2C-1%2C0%2C-4%2C1%29%29\"-(1)det\"%28matrix%282%2C2%2C1%2C1%2C-4%2C1%29%29\"+0=
\n" ); document.write( ".....1(-1)-1(5)=-6
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\n" ); document.write( "s=det s/-6 where matrix s is matrix X with the 1st column replaced by constant coefficents 40,-2,0. I will use column one for our determinant
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\n" ); document.write( "det s = 40 det\"%28matrix%282%2C2%2C-1%2C0%2C-4%2C1%29%29\"-(-2)det\"%28matrix%282%2C2%2C1%2C1%2C-4%2C1%29%29\"
\n" ); document.write( "=40(-1)+2(5)=-30
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\n" ); document.write( "s=det s/-6=\"highlight%28-30%2F-6=5%29\"hours in the soup kitchen
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\n" ); document.write( "t=det t/-6 where matrix t is matrix X with the 2nd column replaced by constant coefficents 40,-2,0. I will use row 3 for our determinant as it has 2 zeros
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\n" ); document.write( "det t=0+0+(1)det\"%28matrix%282%2C2%2C1%2C40%2C1%2C-2%29%29\"=1(-42)=-42
\n" ); document.write( ":
\n" ); document.write( "t=det t/-6=\"highlight%28-42%2F-6=7%29\"hours picking up trash
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\n" ); document.write( ":
\n" ); document.write( "c=det c/-6 where matrix c is matrix X with the 3rd column replaced by constant coefficents 40,-2,0. I will use row 3 for our determinant as it has 2 zeros
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\n" ); document.write( "det c= 0-(-4)\"%28matrix%282%2C2%2C1%2C40%2C1%2C-2%29%29\"+0=4(-42)=-168
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\n" ); document.write( "c=det c/-6=\"highlight%28-168%2F-6=28%29\"hours toy collecting\r
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