document.write( "Question 601391: ASAP:plz
\n" ); document.write( "What is the value of the y variable in the solution to the following system of equations?
\n" ); document.write( "5x + 3y = 7
\n" ); document.write( "3x - 5y = -23 \n" ); document.write( "
Algebra.Com's Answer #379730 by w_parminder(53)\"\" \"About 
You can put this solution on YOUR website!
There are many methods to solve the system of linear equations, but I use the 'elimination method' most of the times.\r
\n" ); document.write( "\n" ); document.write( "In this method, you have to multiply either one or both the equations with an integer in order to make the coefficients of any of the variables in the equations exactly equal to each other. After this, you subtract any of the equation from the other to eliminate that variable.\r
\n" ); document.write( "\n" ); document.write( "5x + 3y = 7 (equation I)
\n" ); document.write( "3x - 5y = -23 (equation II)\r
\n" ); document.write( "\n" ); document.write( "We have to find the value of 'y' only, so I must eliminate 'x' from these equations. To do so, I first find the LCM of the coefficients of 'x' in the equations, i.e. of 5 & 3, which is 15.
\n" ); document.write( "Now we multiply equation I with 3 and equation II with 5 to equate the coefficients of 'x'.\r
\n" ); document.write( "\n" ); document.write( "Now the equations became
\n" ); document.write( "( equation I)*3 => 15x + 9y = 21
\n" ); document.write( "(equation II)*5 => 15x - 25y = -115\r
\n" ); document.write( "\n" ); document.write( "On Subtracting the new equations, we get\r
\n" ); document.write( "\n" ); document.write( "(15x + 9y)-(15x - 25y) = 21 - (-115)
\n" ); document.write( "15x + 9y - 15x + 25y = 21 + 115
\n" ); document.write( "34y = 136\r
\n" ); document.write( "\n" ); document.write( "So y = 136/34 = 4\r
\n" ); document.write( "\n" ); document.write( "This is your required answer, but if you want to find the value of 'x', then put this value of 'y' in any of the given equations and solve it. Let's put this value in equation I\r
\n" ); document.write( "\n" ); document.write( "So equation I => 5x + 3*(4) = 7
\n" ); document.write( "i.e. 5x + 12 = 7
\n" ); document.write( "i.e. 5x = 7 - 12
\n" ); document.write( "i.e. 5x = -5
\n" ); document.write( "i.e. x = -5/5
\n" ); document.write( "i.e. x = -1\r
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\n" ); document.write( "\n" ); document.write( "Please comment if satisfied @ vickywalias@gmail.com
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