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You can put this solution on YOUR website!
your equations are:
\n" ); document.write( "2x+3y+z=13 (equation 1)
\n" ); document.write( "3x+2y+4z=17 (equation 2)
\n" ); document.write( "4x+5y+2z=24 (equation 3)
\n" ); document.write( "multiply equation 1 by -4 and add it to equation 2 to get:
\n" ); document.write( "-8x - 12y -4z = -52 plus:
\n" ); document.write( "3x + 2y + 4z = 17 equals:
\n" ); document.write( "-5x -10y = -35 (equation 4)
\n" ); document.write( "multiply equation 1 by -2 and add it to equation 3 to get:
\n" ); document.write( "-4x - 6y - 2z = -26 plus:
\n" ); document.write( "4x + 5y + 2z = 24 equals:
\n" ); document.write( "-y = -2
\n" ); document.write( "multiply both sides of this equation by -1 to get:
\n" ); document.write( "y = -2
\n" ); document.write( "that's one of the values you are looking for.
\n" ); document.write( "substitute for y in equation 4 to get:
\n" ); document.write( "-5x - 10(2) = -35
\n" ); document.write( "simplify to get:
\n" ); document.write( "-5x - 20 = -35
\n" ); document.write( "add 20 to both sides of the equation to get:
\n" ); document.write( "-5x = -15
\n" ); document.write( "divide both sides of the equation by -5 to get:
\n" ); document.write( "x = 3
\n" ); document.write( "that's the second of the values you are looking for.
\n" ); document.write( "so far you have:
\n" ); document.write( "x = 3
\n" ); document.write( "y = 2
\n" ); document.write( "substitute for x and y in equation 1 to get:
\n" ); document.write( "2(3) + 3(2) + z = 13
\n" ); document.write( "simplify to get:
\n" ); document.write( "6 + 6 + z = 13
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "12 + z = 13
\n" ); document.write( "substract 12 from both sides of the equation to get:
\n" ); document.write( "z = 1
\n" ); document.write( "that's the last of the values you are looking for.
\n" ); document.write( "you have:
\n" ); document.write( "x = 3
\n" ); document.write( "y = 2
\n" ); document.write( "z = 1
\n" ); document.write( "substitute in all 3 original equations to confirm these solutions apply to all of the equations in the system.
\n" ); document.write( "your original equations are:
\n" ); document.write( "2x+3y+z=13
\n" ); document.write( "3x+2y+4z=17
\n" ); document.write( "4x+5y+2z=24
\n" ); document.write( "after substitution, these equations become:
\n" ); document.write( "2(3) + 3(2) + 1 = 13
\n" ); document.write( "3(3) + 2(2) + 4(1) = 17
\n" ); document.write( "4(3) + 5(2) + 2(1) = 24
\n" ); document.write( "after simplification, these equations become:
\n" ); document.write( "6 + 6 + 1 = 13
\n" ); document.write( "9 + 4 + 4 = 17
\n" ); document.write( "12 + 10 + 2 = 24
\n" ); document.write( "after combining like terms, these equations becomes:
\n" ); document.write( "13 = 13
\n" ); document.write( "17 = 17
\n" ); document.write( "24 = 24
\n" ); document.write( "all equations are true confirming the values for x and y and z are good.
\n" ); document.write( "answer is:
\n" ); document.write( "x = 3
\n" ); document.write( "y = 2
\n" ); document.write( "z = 1
\n" ); document.write( " \n" ); document.write( "