document.write( "Question 62171This question is from textbook algebra through applications
\n" ); document.write( ": Can you help me solve these equations using the substitution method?
\n" ); document.write( "1) x-y=15; y=-4x
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\n" ); document.write( "2) 5x+3y=0 ;x+y=0
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\n" ); document.write( "Can you help me solve these equations using the elimination method?\r
\n" ); document.write( "\n" ); document.write( "1) a+b=4; -a+2b=-8
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\n" ); document.write( "2) x+4y=-3; 4x+y=-9 \r
\n" ); document.write( "\n" ); document.write( "3) 8x+2y=3;x-7y=19
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Algebra.Com's Answer #43347 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Can you help me solve these equations using the substitution method?
\n" ); document.write( "1) x - y = 15; y = -4x
\n" ); document.write( ":
\n" ); document.write( "Notice they show y = -4x, therefore we can substitute -4x for y in the 1st
\n" ); document.write( "equation and solve for x:
\n" ); document.write( "x - (-4x) = 15; minus a minus is a plus:
\n" ); document.write( "x + 4x = 15
\n" ); document.write( "5x = 15
\n" ); document.write( ":
\n" ); document.write( "x = 15/5, divided both sides by 5
\n" ); document.write( "x = 3
\n" ); document.write( ":
\n" ); document.write( "Find y by substituting 3 for x:
\n" ); document.write( "y = -4x
\n" ); document.write( "y = -4(3)
\n" ); document.write( "y = -12
\n" ); document.write( ":
\n" ); document.write( "Check our solutions by substituting 3 for x and -12 for y in the 1st equation:
\n" ); document.write( "x - y = 15
\n" ); document.write( "3 - (-12) = 15
\n" ); document.write( "3 + 12 = 15 proves our solutions
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\n" ); document.write( "2) 5x+3y=0 ;x+y=0
\n" ); document.write( "Take the 2nd equation are arrange it in the y = form:
\n" ); document.write( "x + y = 0
\n" ); document.write( "y = -x, subtracted x from both sides:
\n" ); document.write( ":
\n" ); document.write( "Substitute -x for y in the 1st equation:
\n" ); document.write( "5x + 3y = 0
\n" ); document.write( "5x + 3(-x) = 0
\n" ); document.write( "5x - 3x = 0
\n" ); document.write( "Obviously the only value where this could be true is that x = 0 then y = 0 also
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\n" ); document.write( ":
\n" ); document.write( "Can you help me solve these equations using the elimination method?
\n" ); document.write( "In this you arrange the equations in a manner where if they are added or subtracted, one of the unknowns is eliminated,
\n" ); document.write( "1)
\n" ); document.write( " a + b = 4
\n" ); document.write( "-a + 2b = -8
\n" ); document.write( "------------------adding eliminates a:
\n" ); document.write( " 0 + 3b = -4
\n" ); document.write( "b = -4/3
\n" ); document.write( ": Find a, substitute -4/3 for b in the 1st equation:
\n" ); document.write( "a + b = 4
\n" ); document.write( "a +(-4/3) = 4
\n" ); document.write( "a - (4/3) = 4
\n" ); document.write( "a = 4 + (4/3); added (4/3) to both sides:
\n" ); document.write( "a = (12/3) + (4/3); add using common denominator
\n" ); document.write( "a = 16/3
\n" ); document.write( ":
\n" ); document.write( "Check: substitute (-4/3) for b and (16/3) for a in the 2nd equation:
\n" ); document.write( "-a + 3b = -8
\n" ); document.write( "-(16/3) + 2(-4/3) = -8
\n" ); document.write( "-(16/3) - (8/3) = (-24/3) which = -8
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\n" ); document.write( "2)
\n" ); document.write( " x + 4y = -3
\n" ); document.write( "4x + y = -9\r
\n" ); document.write( "\n" ); document.write( "Mult the 1st equation by 4, leave the 2nd equation as it is:
\n" ); document.write( " 4x + 16y = -12
\n" ); document.write( " 4x + y = -9
\n" ); document.write( "---------------------Subtracting eliminates x:
\n" ); document.write( " 0x + 15y = -3
\n" ); document.write( "y = -3/15
\n" ); document.write( "y = -1/5 or -.2
\n" ); document.write( ":
\n" ); document.write( "Find x: Substitute =.2 for y in the 1st equation
\n" ); document.write( "x + 4y = -3
\n" ); document.write( "x + 4(-.2) = -3
\n" ); document.write( "x - .8 = -3
\n" ); document.write( "x = -3 + .8
\n" ); document.write( "x = -2.2
\n" ); document.write( ":
\n" ); document.write( "Check our solution in the 2nd equation:
\n" ); document.write( "4x + y = -9
\n" ); document.write( "4(-2.2) + (-.2) = -9
\n" ); document.write( "-8.8 - .2 = -9 checks out our solutions:
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\n" ); document.write( "3)
\n" ); document.write( "8x + 2y = 3
\n" ); document.write( " x - 7y = 19
\n" ); document.write( ":
\n" ); document.write( "Mult the 2nd equation by 8:
\n" ); document.write( "8x + 2y = 3
\n" ); document.write( "8x -56y = 152
\n" ); document.write( "--------------Subtracting eliminates x:
\n" ); document.write( "0x + 58y = - 149
\n" ); document.write( "y = -149/58; a nasty fraction
\n" ); document.write( ":
\n" ); document.write( "Find x using the 1st equation
\n" ); document.write( "8x + 2y = 3
\n" ); document.write( "8x +2(-149/58) = 3
\n" ); document.write( "8x - 298/58 = 3
\n" ); document.write( "Get rid of the denominator, mult eq by 58:
\n" ); document.write( "464x - 298 = 174
\n" ); document.write( "464x = 174 + 298
\n" ); document.write( "464x = 472
\n" ); document.write( "x = 472/464
\n" ); document.write( "x = 59/58
\n" ); document.write( ":
\n" ); document.write( "Check using the 2nd equation
\n" ); document.write( "x - 7y = 19
\n" ); document.write( "(59/58) - 7(-149/58) = 19
\n" ); document.write( "(59/58) + 1043/58 = 19 = 19
\n" ); document.write( "1102/58 = 19
\n" ); document.write( "19 = 19, proves these nasty fractions are indeed the solutions!\r
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