document.write( "Question 156745: 2x-2y=15
\n" ); document.write( "4x+4y=10\r
\n" ); document.write( "\n" ); document.write( "Help, I need to solve for x and y
\n" ); document.write( "

Algebra.Com's Answer #115581 by Electrified_Levi(103)\"\" \"About 
You can put this solution on YOUR website!
Hi, Hope I can help,
\n" ); document.write( ".
\n" ); document.write( "2x-2y=15
\n" ); document.write( "4x+4y=10
\n" ); document.write( "Help, I need to solve for x and y
\n" ); document.write( ".
\n" ); document.write( "First, you can reduce the second equation, by multiplying each side by \"2\"
\n" ); document.write( ".
\n" ); document.write( "\"4x%2B4y=10\" = \"%284x%2B4y%29%2F2=10%2F2\" = \"%284x%2B4y%29%2F2=10%2F2\" = \"%284x%29%2F2%2B%284y%29%2F2=10%2F2\" = \"2x%2B2y=5\"
\n" ); document.write( ".
\n" ); document.write( "The second equation \"+4x%2B4y=10+\" is reduced to \"+2x%2B2y=5+\"
\n" ); document.write( ".
\n" ); document.write( "The Two equations are
\n" ); document.write( ".
\n" ); document.write( "\"+2x-2y=15+\"
\n" ); document.write( ".
\n" ); document.write( "\"+2x%2B2y=5+\"
\n" ); document.write( ".
\n" ); document.write( "This is the way I usually solve these equations, First, solve for a letter(usually the easiest letter), we will solve for \"x\" in both equations
\n" ); document.write( ".
\n" ); document.write( "Equation 1 = \"+2x-2y=15+\"
\n" ); document.write( ".
\n" ); document.write( "Now we will move (-2y) to the right side
\n" ); document.write( ".
\n" ); document.write( "\"+2x-2y=15+\" = \"+2x-2y+%2B+2y=15+%2B+2y+\" = \"+2x+=+15+%2B+2y+\"
\n" ); document.write( ".
\n" ); document.write( "We will rearrange the numbers
\n" ); document.write( ".
\n" ); document.write( "\"+2x+=+15+%2B+2y+\" = \"+2x+=+2y+%2B+15+\"
\n" ); document.write( ".
\n" ); document.write( "We will divide each side by \"2\" to get \"x\"
\n" ); document.write( ".
\n" ); document.write( "\"+2x%2F2+=+%282y+%2B+15%29%2F2+\" = \"+x+=+%282y+%2B+15%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "Our first \"x\" = \"+%282y+%2B+15%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "Now let's solve \"x\" in our second equation, \"+2x%2B2y=5+\"
\n" ); document.write( ".
\n" ); document.write( "We will move (2y) to the right side
\n" ); document.write( ".
\n" ); document.write( "\"+2x%2B2y=5+\" = \"+2x%2B2y+-+2y=5+-2y+\" = \"+2x=+5+-2y+\"
\n" ); document.write( ".
\n" ); document.write( "We will rearrange the numbers
\n" ); document.write( ".
\n" ); document.write( "\"+2x=+5+-2y+\" = \"+2x=+%28-2y%29+%2B+5+\"
\n" ); document.write( ".
\n" ); document.write( "We will divide each side by \"2\" to get \"x\"
\n" ); document.write( ".
\n" ); document.write( "\"+2x=+%28-2y%29+%2B+5+\" = \"+2x%2F2=+%28%28-2y%29+%2B+5%29%2F2+\" = \"+x=+%28%28-2y%29+%2B+5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "Our second \"x\" = \"+%28%28-2y%29+%2B+5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "Since \"x\" is one number, and \"x\" equals our two answers, our answers equal each other, we can put our two answers in an equation
\n" ); document.write( ".
\n" ); document.write( "Answer 1 = \"+%282y+%2B+15%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "Answer 2 = \"+%28%28-2y%29+%2B+5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "\"+%282y%2B15%29%2F2+=+%28%28-2y%29+%2B+5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "We will now solve for \"y\"
\n" ); document.write( ".
\n" ); document.write( "\"+%282y%2B15%29%2F2+=+%28%28-2y%29+%2B+5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "We will use cross multiplication
\n" ); document.write( ".
\n" ); document.write( "\"+highlight%282y%2B15%29%2F2+=+%28%28-2y%29+%2B+5%29%2Fhighlight%282%29+\" = \"+%282y%2B15%29%2Fhighlight%282%29+=+highlight%28%28-2y%29+%2B+5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "It will become \"+%282y%2B15%29%282%29+=+%282%29%28%28-2y%29%2B5%29+\"
\n" ); document.write( ".
\n" ); document.write( "We will rearrange numbers
\n" ); document.write( ".
\n" ); document.write( "\"+%282y%2B15%29%282%29+=+%282%29%28%28-2y%29%2B5%29+\" = \"+%282%29%282y%2B15%29+=+%282%29%28%28-2y%29%2B5%29+\"
\n" ); document.write( ".
\n" ); document.write( "We will use the distribution method
\n" ); document.write( ".
\n" ); document.write( " =
\n" ); document.write( ".
\n" ); document.write( " =
\n" ); document.write( ".
\n" ); document.write( "\"+4y+%2B+30+=+%28-4y%29+%2B+10+\"
\n" ); document.write( ".
\n" ); document.write( "Now we will solve for \"y\", we will move (-4y) to the left
\n" ); document.write( ".
\n" ); document.write( "\"+4y+%2B+30+=+%28-4y%29+%2B+10+\" = \"+4y+%2B+4y+%2B+30+=+%28-4y%29+%2B+4y+%2B+10+\" = \"+8y+%2B+30+=+10+\"
\n" ); document.write( ".
\n" ); document.write( "Now we will move (30) to the right side
\n" ); document.write( ".
\n" ); document.write( "\"+8y+%2B+30+=+10+\" = \"+8y+%2B+30+-30+=+10+-30+\" = \"+8y+=+%28-20%29+\"
\n" ); document.write( ".
\n" ); document.write( "Now to find \"y\" we will divide each side by \"8\"
\n" ); document.write( ".
\n" ); document.write( "\"+8y+=+%28-20%29+\" = \"+8y%2F8+=+%28-20%29%2F8+\" = \"+y+=+%28-20%29%2F8+\", if we reduce \"+y+=+%28-5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "y = \"+%28-5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "To find \"x\" all you do is substitute \"y\" with \"+%28-5%29%2F2+\" in one of our original equations
\n" ); document.write( ".
\n" ); document.write( "\"+2x-2y=15+\"
\n" ); document.write( ".
\n" ); document.write( "\"+2x%2B2y=5+\"
\n" ); document.write( ".
\n" ); document.write( "Let's use the second equation(replace \"y\" with \"+%28-5%29%2F2+\" )
\n" ); document.write( ".
\n" ); document.write( "\"+2x%2B2y=5+\" = \"+2x%2B2%28%28-5%29%2F2%29=5+\" = \"+2x%2B%28-5%29=5+\" = \"+2x-5+=5+\"
\n" ); document.write( ".
\n" ); document.write( "We will move (-5) over to the right side
\n" ); document.write( ".
\n" ); document.write( "\"+2x-5+=5+\" = \"+2x-5+%2B+5+=5+%2B+5+\" = \"+2x+=10+\"
\n" ); document.write( ".
\n" ); document.write( "Now we will divide each side by \"2\" to get \"x\"
\n" ); document.write( ".
\n" ); document.write( "\"+2x%2F2+=10%2F2+\" = \"+x+=10%2F2+\" = \"+x+=5+\"
\n" ); document.write( ".
\n" ); document.write( "x = \"+5+\"
\n" ); document.write( ".
\n" ); document.write( "We can check our answers by replacing \"x\" and \"y\" with our answers we got, in our very first equations
\n" ); document.write( ".
\n" ); document.write( "x = \"+5+\"
\n" ); document.write( ".
\n" ); document.write( "y = \"+%28-5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "Let's replace \"x\" and \"y\" with the numbers above
\n" ); document.write( ".
\n" ); document.write( "\"+2x-2y=15+\" = \"+2%285%29-2%28%28-5%29%2F2%29%29=15+\" = \"+10+-%28-5%29=15+\" = \"+10+%2B5+=15+\" = \"+15+=15+\" (True)
\n" ); document.write( ".
\n" ); document.write( "\"+4x%2B4y=10+\" = \"+4%285%29%2B4%28%28-5%29%2F2%29=10+\" = \"+20%2B%28-10%29=10+\" = \"+20-10=10+\" = \"+10=10+\" (True)
\n" ); document.write( ".
\n" ); document.write( "This method will work for all problems like this
\n" ); document.write( ".
\n" ); document.write( "x = \"+5+\"
\n" ); document.write( ".
\n" ); document.write( "y = \"+%28-5%29%2F2+\"
\n" ); document.write( ".
\n" ); document.write( "The ordered pair is (x,y), our ordered pair is (5, \"+%28-5%29%2F2+\" )
\n" ); document.write( ".
\n" ); document.write( "Hope I helped, Levi
\n" ); document.write( "
\n" );