document.write( "Question 1043640: (a-2)x+(b+2)y=8
\n" ); document.write( "bx+ay=4
\n" ); document.write( "In the system of equations above a and b are constants. If the system has infinitely many solutions, what is the value of a ?
\n" ); document.write( "A) -4/3
\n" ); document.write( "B) -2/3
\n" ); document.write( "C) 2/3
\n" ); document.write( "D) 4/3 \n" ); document.write( "

Algebra.Com's Answer #658794 by ikleyn(52839) $\"\"$ $\"About$

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\n" ); document.write( "(a-2)x+(b+2)y=8
\n" ); document.write( "bx+ay=4
\n" ); document.write( "In the system of equations above a and b are constants. If the system has infinitely many solutions, what is the value of a ?
\n" ); document.write( "A) -4/3
\n" ); document.write( "B) -2/3
\n" ); document.write( "C) 2/3
\n" ); document.write( "D) 4/3
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document.write( "(a-2)x + (b+2)y = 8,   (1)\r\n" );
document.write( "    bx +     ay = 4.   (2)\r\n" );
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document.write( "In order for the system (1),(2) had infinitely many solutions,\r\n" );
document.write( "this condition should be in place:\r\n" );
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document.write( "    the ratio of coefficients at \"x\" is equal to the ratio of coefficients \r\n" );
document.write( "    at \"y\" AND equal to the ratio of right sides \r\n" );
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document.write( "(assuming that the system is written in canonical form, as (1) and (2)).\r\n" );
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document.write( "This condition, applied to the system (1),(2) has the form\r\n" );
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document.write( " =  = 2.\r\n" );
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document.write( "So, you have these two equations (actually, the system of two equations)\r\n" );
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document.write( " = 2,   (3)\r\n" );
document.write( " = 2    (4)\r\n" );
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document.write( "to determine two unknowns \"a\" and \"b\". Simplify this system:\r\n" );
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document.write( "a - 2 = 2b,          (3')\r\n" );
document.write( "b + 2 = 2a.          (4')\r\n" );
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document.write( "You can solve it by using the substitution method.\r\n" );
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document.write( "Can you do it on your own?\r\n" );
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\n" ); document.write( "\n" ); document.write( "For linear systems of two equations in two unknowns see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of a linear system of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "    - Solving word problems using linear systems of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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