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Solve the system by addition or substitution.
\n" ); document.write( " 3x – 4y = 8 ----(1)
\n" ); document.write( " 6x – 2y = 10 ----(2)X 2
\n" ); document.write( "(Observing that the coefficients of y are (-4) and (-2) respectively, inorder to equalise the coefficients of y we find the lcm of 4 and 2 which is 4 and hence multiplying (2) through out by 2 and then subtracting the two equations we get rid of the variable y and arrive at a single simple equation in x)
\n" ); document.write( " 3x – 4y = 8 ----(1)
\n" ); document.write( " 12x – 4y = 20 ----(3)
\n" ); document.write( "(3) - (1) gives
\n" ); document.write( "(12x-3x)+[(-4y) - (-4y)] = 20-8
\n" ); document.write( "(in tests and exams you may simply do vertical subtraction mentally and write)
\n" ); document.write( " 9x+0 = 12
\n" ); document.write( "9x = 12
\n" ); document.write( "x = 12/9 = 4/3
\n" ); document.write( "Putting x = 4/3 in (2), 6x-2y = 10 ----(2)
\n" ); document.write( "6X(4/3)-2y = 10
\n" ); document.write( "8-10 = 2y
\n" ); document.write( "-2 = 2y
\n" ); document.write( "y = (-2)/2 = -1
\n" ); document.write( "Therefore x =(4/3) and y = -1
\n" ); document.write( "Verification: We have put x in (2) to find y
\n" ); document.write( "So use (1) for verification.
\n" ); document.write( "Put x =(4/3) and y = -1 in (1)which is 3x – 4y = 8 ----(1)
\n" ); document.write( "LHS = 3x-4y = 3X(4/3) -4X(-1) = 4+4 = 8 = RHS
\n" ); document.write( "Therefore our values are correct\r
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