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I need help using the substitution method so can you help me solve this problem:
\n" ); document.write( "3x+5y=-3
\n" ); document.write( "-3x+y=-15
\n" ); document.write( "I also need help using the combination method so maybe with these too:
\n" ); document.write( "1) 4x+5y=-2
\n" ); document.write( " 5x=5-10y
\n" ); document.write( "2) 3y=16-2x
\n" ); document.write( " 5x+2y=14\r
\n" ); document.write( "\n" ); document.write( "Last question is on graphing inequalities, i think:
\n" ); document.write( "4x+3y (is less than or equal to) 13
\n" ); document.write( "-3x+4y(is greater than or equal to) 9\r
\n" ); document.write( "\n" ); document.write( "1)Substitution method:
\n" ); document.write( " 3x+5y=-3 ----(1)
\n" ); document.write( "-3x+y=-15 ----(2)
\n" ); document.write( "From (2), we have y = 3x-15 ----(*)
\n" ); document.write( "(adding 3x to both the sides or transferring -3x from LHS to RHS, change side then change sign)
\n" ); document.write( "Substituting for y in (1),
\n" ); document.write( "3x + 5(3x-15) = -3
\n" ); document.write( "3x +5X3x - 5X15 = -3
\n" ); document.write( "3x+15x -75 =-3
\n" ); document.write( "18x = -3+75
\n" ); document.write( "18x = 72
\n" ); document.write( "x = 72/18 = (18X4)/18 = 4
\n" ); document.write( "Putting x= 4 in (*),
\n" ); document.write( "y = 3x - 15
\n" ); document.write( " = 3X4 - 15 = 12-15 = -3
\n" ); document.write( "Answer: x=4 and y = -3
\n" ); document.write( "Verification: We have used (2) for our finding the variables.So we use (1)for verification.
\n" ); document.write( "Putting x=4 and y = -3 in (1)
\n" ); document.write( "3x+5y=-3 ----(1)
\n" ); document.write( "LHS = 3X4 +5X(-3) = 12-15 = -3 =RHS
\n" ); document.write( "Therefore our values are correct.\r
\n" ); document.write( "\n" ); document.write( "I also need help using the combination method so maybe with these too:
\n" ); document.write( "1) 4x+5y=-2
\n" ); document.write( " 5x=5-10y
\n" ); document.write( "2) 3y=16-2x
\n" ); document.write( " 5x+2y=14\r
\n" ); document.write( "\n" ); document.write( "Combination method:
\n" ); document.write( "1) 4x+5y=-2
\n" ); document.write( " 5x=5-10y
\n" ); document.write( "First of all see to it that both the equations are in the form Ax+By = C
\n" ); document.write( "The given equations are
\n" ); document.write( "4x+5y=-2 ----(1)X 2
\n" ); document.write( "5x+10y= 5 ----(2) (bringing -10y from the right side to the left side)
\n" ); document.write( "Observe that 5 and 10 are the coefficients of y respectively in the equations.
\n" ); document.write( "And their lcm is 10.
\n" ); document.write( "Why take the lcm? It is for equalising the coefficients of the variable we want to eliminate.
\n" ); document.write( "Since 5X2 = 10, multiply equation (1) through out by 2
\n" ); document.write( "8x+10y=-4 ----(3)
\n" ); document.write( "5x+10y= 5 ----(2)
\n" ); document.write( "(3) - (2)gives
\n" ); document.write( "(8x-5x) + 0 = (-4-5) (you may do vertical subtraction and get the answer faster)
\n" ); document.write( "3x = -9
\n" ); document.write( "x = -9/3 = -3
\n" ); document.write( "Putting x= -3 in (1),
\n" ); document.write( "4x+5y=-2 ----(1)
\n" ); document.write( "4X(-3) + 5y = -2
\n" ); document.write( "-12+5y = -2
\n" ); document.write( "5y = +12-2
\n" ); document.write( "5y = 10
\n" ); document.write( "y = 10/5 = 2
\n" ); document.write( "Answer: x = -3 and y = 2
\n" ); document.write( "Verification:Putting x = -3 and y = 2 in (2)
\n" ); document.write( "5x+10y= 5 ----(2)
\n" ); document.write( "LHS = 5x+10y
\n" ); document.write( "= 5X(-3)+10X2
\n" ); document.write( "=-15+20
\n" ); document.write( "=+5 =RHS which is correct\r
\n" ); document.write( "\n" ); document.write( "2) 3y=16-2x
\n" ); document.write( " 5x+2y=14
\n" ); document.write( "The given equation are
\n" ); document.write( " 2x+3y = 16 ----(1)X 2
\n" ); document.write( " 5x+2y = 14 ----(2)X 3
\n" ); document.write( "(lcm of the coefficients of y is 6)
\n" ); document.write( " 4x + 6y = 32 ----(3)
\n" ); document.write( "15x + 6y = 42 ----(4)
\n" ); document.write( "(3) - (4)implies
\n" ); document.write( "(4x-15x)+ (6y - 6y) = 32 - 42
\n" ); document.write( " -11x +0 = -10
\n" ); document.write( "-11x = -10
\n" ); document.write( "x = (-10)(-11) = 10/11
\n" ); document.write( "x=10/11 in (1)gives
\n" ); document.write( "2X(10/11) + 3y = 16
\n" ); document.write( "20/11 + 3y = 16
\n" ); document.write( "3y = 16-20/11
\n" ); document.write( "3y = (16X11-20)/11
\n" ); document.write( "3y = (176-20)/11
\n" ); document.write( "3y = 156/11
\n" ); document.write( "y = (3X52)/(3X11)
\n" ); document.write( "y = 52/11
\n" ); document.write( "Answer: x =10/11 and y = 52/11
\n" ); document.write( "Verification: Putting x =10/11 and y = 52/11 in 5x+2y = 14 ----(2)
\n" ); document.write( "LHS = 5x+2y
\n" ); document.write( "=5x(10/11) + 2X(52/11)
\n" ); document.write( "= 50/11 +104/11 =(50+104)/11 = 154/11 = (11X14)/11 = 14 =RHS which is correct
\n" ); document.write( "PLEASE NOTE:
\n" ); document.write( "The inequality problem has symbols like less than or equal to and greater than or equal and hence I have done the problem under a different application and I tried to copy it using print screen, copy, paste feature. It does not seem to work.Hence if you could give me your email address may be my attachment will work.\r
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