document.write( "Question 102774This question is from textbook
\n" ); document.write( ": Please help me with this problem\r
\n" ); document.write( "\n" ); document.write( "Solve the system by addition method\r
\n" ); document.write( "\n" ); document.write( "Eq 1 states: 3x + 3y = 33
\n" ); document.write( "Eq 2 states: 5x - 2y = 27\r
\n" ); document.write( "\n" ); document.write( "I appreciate any help you can give me \n" ); document.write( "
Algebra.Com's Answer #74761 by doukungfoo(195)\"\" \"About 
You can put this solution on YOUR website!
The objective when using the addition method is to eliminate one of the variables in the system of equations.
\n" ); document.write( "The first equation has a postive 3y
\n" ); document.write( "and the second has a negative 2y
\n" ); document.write( "so the y variable is the one we will eliminate.
\n" ); document.write( "but before we can do this we have to get y's coefficients to equal one another.
\n" ); document.write( "to do this we will multiply the first equation by 2
\n" ); document.write( "and then multiply the second equation by 3
\n" ); document.write( "so lets do that
\n" ); document.write( "3x + 3y = 33
\n" ); document.write( "multiply each term by 2
\n" ); document.write( "2(3x) + 2(3y) = 2(33)
\n" ); document.write( "6x + 6y = 66
\n" ); document.write( "now lets take the second equation and multiply each term by 3
\n" ); document.write( "5x - 2y = 27
\n" ); document.write( "3(5x) - 3(2y) = 3(27)
\n" ); document.write( "15x - 6y = 81
\n" ); document.write( "ok so now our system of equations looks like this
\n" ); document.write( "6x + 6y = 66
\n" ); document.write( "15x - 6y = 81
\n" ); document.write( "now we are ready to use the addition method
\n" ); document.write( "6x + 15x = 21x
\n" ); document.write( "6y + (-6y) = 0
\n" ); document.write( "66 + 81 = 147
\n" ); document.write( "that leaves us with
\n" ); document.write( "21x = 147
\n" ); document.write( "solve for x
\n" ); document.write( "21x/21 = 147/21
\n" ); document.write( "x = 7
\n" ); document.write( "So now the we have found x = 7
\n" ); document.write( "we can use this value for x in either of the original equations to solve for y
\n" ); document.write( "3x + 3y = 33
\n" ); document.write( "3(7) + 3y = 33
\n" ); document.write( "21 + 3y = 33
\n" ); document.write( "21 - 21 + 3y = 33 - 21
\n" ); document.write( "3y = 12
\n" ); document.write( "3y/3 = 12/3
\n" ); document.write( "y = 4
\n" ); document.write( "Answer: So our solution is x = 7 and y = 4
\n" ); document.write( "Check solutions by seeing if they satisfy both original equations:
\n" ); document.write( "3x + 3y = 33
\n" ); document.write( "3(7) + 3(4) = 33
\n" ); document.write( "21 + 12 = 33
\n" ); document.write( "33 = 33
\n" ); document.write( "AND
\n" ); document.write( "5x - 2y = 27
\n" ); document.write( "5(7) - 2(4) = 27
\n" ); document.write( "35 - 8 = 27
\n" ); document.write( "27 = 27
\n" ); document.write( "They both work so we know we have solved the system of equations correctly and we use the addition method to do it.\r
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