document.write( "Question 29122: Solve the system.
\n" ); document.write( " x + 2y = –15
\n" ); document.write( " –2x + 4y = 6
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #15922 by sdmmadam@yahoo.com(530)\"\" \"About 
You can put this solution on YOUR website!
Solve the system.
\n" ); document.write( " x + 2y = –15 ----(1)X 2
\n" ); document.write( " –2x + 4y = 6 ----(2)
\n" ); document.write( " 2x + 4y = -30 ----(3)(got by multiplying (1) by 2)
\n" ); document.write( "(2)+(3) implies
\n" ); document.write( " (4y +4y) =(6)+(-30)
\n" ); document.write( " 8y = -24
\n" ); document.write( "y = -24/8 = -3
\n" ); document.write( "y=-3 in (1) implies
\n" ); document.write( "x+2y =-15
\n" ); document.write( "x+2X(-3) = - 15
\n" ); document.write( "x-6 = -15
\n" ); document.write( "x= -15+6
\n" ); document.write( "x=-9
\n" ); document.write( "Answer: x=-9 and y= -3
\n" ); document.write( "Verification: Putting x=-9 and y=-3 in the other equation (2)
\n" ); document.write( "LHS = -2x+4y = -2X(-9)+4X(-3) = +18-12 = 6 =RHS
\n" ); document.write( "Therefore our values are correct
\n" ); document.write( "Note: Why did we multiply (1) by 2 and get (3)
\n" ); document.write( "To equalise the coefficients of x numerically so that we can add the resulting equation (3) with (2) and get rid of x.
\n" ); document.write( "Why did we have to add? why not subtract?
\n" ); document.write( "We add when the coefficients are equal in magnitude and opposite in sign
\n" ); document.write( "(we subtract when the coefficients are equal in magnitude and in sign also)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );