document.write( "Question 155953: 0.3x-0.2y=4
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Algebra.Com's Answer #114901 by Electrified_Levi(103)\"\" \"About 
You can put this solution on YOUR website!
Hi, Hope I can help
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\n" ); document.write( "\"+0.3x-0.2y=4+\"
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\n" ); document.write( "\"+0.2x%2B0.5y=%28-3%29+\"
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\n" ); document.write( "If you are trying to find the solution to the two equations, this is the way I do it.
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\n" ); document.write( "First, we will multiply each equation by 10(multiply each side of the two equations by 10)(you don't have to, but it will get rid of the decimal point)
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\n" ); document.write( "We will multiply
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\n" ); document.write( "First equation = \"+0.3x-0.2y=4+\" = \"+10%280.3x-0.2y%29=%2810%294+\" = \"+3x+-+2y+=+40+\"
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\n" ); document.write( "Second equation = \"+0.2x%2B0.5y=-3+\" = \"+10%280.2x%2B0.5y%29=%2810%29%28-3%29+\" = \"+2x+%2B+5y+=+%28-30%29+\"
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\n" ); document.write( "The two new equations \"+%28original-equations%29%2810%29+\" are
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\n" ); document.write( "First equation = \"+3x+-+2y+=+40+\"
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\n" ); document.write( "Second equation = \"+2x+%2B+5y+=+%28-30%29+\"
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\n" ); document.write( "Now we can start solving
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\n" ); document.write( "First, solve for a letter in each equation(doesn't matter which letter) we will solve for \"x\"
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\n" ); document.write( "First equation = \"+3x+-+2y+=+40+\"
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\n" ); document.write( "We will move (-2y) to the right side
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\n" ); document.write( "\"+3x+-+2y+%2B+2y+=+40+%2B+2y+\" = \"+3x+=+40+%2B+2y+\"
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\n" ); document.write( "We will rearrange the right side
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\n" ); document.write( "\"+3x+=+40+%2B+2y+\" = \"+3x+=+2y+%2B+40+\"
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\n" ); document.write( "We will divide by \"3\" to get \"x\"
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\n" ); document.write( "\"+3x%2F3+=+%282y+%2B+40%29%2F3+\" = \"+x+=+%282y+%2B+40%29%2F3+\"
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\n" ); document.write( "Our first answer = \"+%282y+%2B+40%29%2F3+\"
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\n" ); document.write( "Now we will solve our second equation \"+2x+%2B+5y+=+%28-30%29+\"
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\n" ); document.write( "We will move \"5y\" to the right side
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\n" ); document.write( "\"+2x+%2B+5y+-+5y+=+%28-30%29+-+5y+\" = \"+2x+=+%28-30%29+-+5y+\"
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\n" ); document.write( "If we rearrange we will get \"+2x+=+%28-5y%29+-+30+++\"
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\n" ); document.write( "We need to divide by \"2\" to get \"x\"
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\n" ); document.write( "\"+2x%2F2+=+%28%28-5y%29+-+30%29%2F2+++\" = \"+x+=+%28%28-5y%29+-+30%29%2F2+\"
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\n" ); document.write( "Our second answer = \"+%28%28-5y%29+-+30%29%2F2+\"
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\n" ); document.write( "Our two answers we got are
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\n" ); document.write( "Answer 1 = \"+%282y+%2B+40%29%2F3+\"
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\n" ); document.write( "Answer 2 = \"+%28%28-5y%29+-+30%29%2F2+\"
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\n" ); document.write( "We will now put the two answers together in an equation (since they equal the same letter \"x\", they equal each other)
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\n" ); document.write( "\"+%282y+%2B+40%29%2F3+=+%28%28-5y%29+-+30%29%2F2+\"
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\n" ); document.write( "Now we will start solving for \"y\", we will cross multiply
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\n" ); document.write( "\"+highlight%282y+%2B+40%29%2F3+=+%28%28-5y%29+-+30%29%2Fhighlight%282%29+\"
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\n" ); document.write( "\"+%282y+%2B+40%29%2Fhighlight%283%29+=+highlight%28%28-5y%29+-+30%29%2F2+\"
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\n" ); document.write( "we will get \"+2%282y+%2B+40%29+=+3%28%28-5y%29+-+30%29+\"
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\n" ); document.write( "when we use distribution, we get \"+4y+%2B+80+=+%28-15y%29+-+90+\"
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\n" ); document.write( "We will move (-15y) to the left
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\n" ); document.write( "\"+4y+%2B+15y+%2B+80+=+%28-15y%29+%2B+15y+-+90+\" = \"+19y+%2B+80+=+%28-90%29+\"
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\n" ); document.write( "\"+19y+%2B+80+=+%28-90%29+\"
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\n" ); document.write( "We will move the \"80\" to the right
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\n" ); document.write( "\"+19y+%2B+80+-+80+=+%28-90%29+-+80+\" = \"+19y+=+%28-170%29+\"
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\n" ); document.write( "We will now divide each side by \"19\" to get \"y\"
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\n" ); document.write( "\"+19y%2F19+=+%28-170%29%2F19+\" = \"+y+=+%28-170%29%2F19+\"
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\n" ); document.write( "We found that \"y\" = \"+%28-170%29%2F19+\"
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\n" ); document.write( "We can replace \"y\" with \"+%28-170%29%2F19+\" in one of our easier equations( one of the \"+%28original+-+equations%29%2810%29+\" equations
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\n" ); document.write( "\"+3x+-+2y+=+40+\"
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\n" ); document.write( "\"+2x+%2B+5y+=+%28-30%29+\"
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\n" ); document.write( "We will use the first equation(replace \"y\" with \"+%28-170%29%2F19+\"
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\n" ); document.write( "\"+3x+-+2y+=+40+\"
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\n" ); document.write( "\"+3x+-+2%28-170%2F19%29+=+40+\"
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\n" ); document.write( "\"+3x+-+%28-340%2F19%29+=+40+\"
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\n" ); document.write( "double negative
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\n" ); document.write( "\"+3x+%2B+%28340%2F19%29+=+40+\"
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\n" ); document.write( "we will move \"+%28340%2F19%29+\" to the right side
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\n" ); document.write( "\"+3x+%2B+%28340%2F19%29+-+%28340%2F19%29+=+40+-+%28340%2F19%29+\" = \"+3x+=+40+-+%28340%2F19%29+\"
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\n" ); document.write( "we need to change the \"40\" , 40 = \"+760%2F19+\", replace \"40\" with that number
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\n" ); document.write( "\"+3x+=+%28760%2F19%29+-+%28340%2F19%29+\"
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\n" ); document.write( "\"+3x+=+%28760+-+340%29%2F19%29+\" = \"+3x+=+420%2F19+\"
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\n" ); document.write( "No we will divide each side by \"3\" to get our answer
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\n" ); document.write( "\"+3x%2F3+=+%28420%2F19%29%2F3+\" = \"+x+=+420%2F57+\" = \"+x+=+140%2F19+\"
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\n" ); document.write( "Our \"x\" = \"+140%2F19+\", we can check our solution in one of our original equations(our very first two equations)
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\n" ); document.write( "Equation 1 = \"+0.3x-0.2y=4+\"
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\n" ); document.write( "Equation 2 = \"+0.2x%2B0.5y=%28-3%29+\"
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\n" ); document.write( "\"x\" = \"+140%2F19+\"
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\n" ); document.write( "\"y\" = \"+%28-170%29%2F19+\"
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\n" ); document.write( "We will replace \"x\" and \"y\"
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\n" ); document.write( "Equation 1 = \"+0.3%28140%2F19%29+-+0.2%28%28-170%29%2F19%29+=4+\"( 0.3 same as \"%283%2F10%29+\")(0.2 same as \"+%282%2F10%29+\"
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\n" ); document.write( "\"+%28420%2F190%29+%2B+%28340%2F190%29+=4+\" = \"+760%2F190+=4+\"
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\n" ); document.write( "\"+4+=4+\" (True)
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\n" ); document.write( "We can replace \"x\" and \"y\" in our second equation ( 0.2 = \"2%2F10+\", 0.5 = \"+5%2F10+\" = \"+1%2F2+\" ) ( we will use \"+5%2F10+\" )
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\n" ); document.write( "\"+0.2x%2B0.5y=%28-3%29+\"
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\n" ); document.write( "\"+0.2%28140%2F19%29%2B0.5%28-170%2F19%29=%28-3%29+\"
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\n" ); document.write( "\"+%28280%2F190%29%2B+%28%28-850%29%2F190%29=%28-3%29+\"
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\n" ); document.write( "\"+%28280%2F190%29+-+%28%28850%29%2F190%29=%28-3%29+\"
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\n" ); document.write( "\"+%28-570%29%2F190=+%28-3%29+\" = \"+%28-3%29+=+%28-3%29+\" True
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\n" ); document.write( "\"x\" = \"+140%2F19+\" or 7 \"+7%2F19+\"
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\n" ); document.write( "\"y\" = \"+%28-170%29%2F19+\" or ( -8 \"+18%2F19+\" )
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\n" ); document.write( "solution set = (x,y), our solution set = (\"+140%2F19+\", \"+%28-170%29%2F19+\" )
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\n" ); document.write( "Hope I helped,Levi
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