document.write( "Question 1156102: 1. Solve the given system by Cramer’s Rule :
\n" ); document.write( "5x1+ 4x2 = -14
\n" ); document.write( "3x1+ 6x2 = 6 \n" ); document.write( "

Algebra.Com's Answer #778791 by ikleyn(52943) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "First, calculate the determinant of the coefficient matrix\r\n" );
document.write( "\r\n" );
document.write( "    D = det  = 5*6 - 3*4 = 30 - 12 = 18.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, calculate the determinant Dx, replacing first column in the coefficient matrix by the right side vector\r\n" );
document.write( "\r\n" );
document.write( "    Dx = det  = -14*6 - 4*6 = -84 - 24 = -108.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, calculate the determinant Dy, replacing second column in the coefficient matrix by the right side vector\r\n" );
document.write( "\r\n" );
document.write( "    Dy = det  = 5*6 - (-14)*3 = 30 - (-42) = 72.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the solution is  x =  =  = -6;  y =  =  = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  x = -6,  y = 4.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On Cramer's rule for solving 2x2-system of equations, see the lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "and the lessons\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    - What is a matrix? \r
\n" ); document.write( "\n" ); document.write( "    - Determinant of a 2x2-matrix \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule) \r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of linear equations in two unknowns using the Cramer's rule \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );