document.write( "Question 1190891: The solution to this system of equations is (-2, 3). Find the values of p and q. [4]
\n" ); document.write( "px+qy=13
\n" ); document.write( "qx+(p+1)y=1 \n" ); document.write( "
Algebra.Com's Answer #822621 by Theo(13342)\"\" \"About 
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your equations are:
\n" ); document.write( "px + qy = 13
\n" ); document.write( "qx + (p+1)y = 1
\n" ); document.write( "the solution is (-2,3).
\n" ); document.write( "that means that x = -2 and y = 3.
\n" ); document.write( "replace x and y with these values in the equation to get:
\n" ); document.write( "-2 * p + 3 * q = 13
\n" ); document.write( "-2 * q + 3 * (p + 1) = 1
\n" ); document.write( "simplify the second equation to get:
\n" ); document.write( "-2 * q + 3 * p + 3 = 1
\n" ); document.write( "subtract 3 from both sides to get:
\n" ); document.write( "-2 * q + 3 * p = -2
\n" ); document.write( "rearrange the terms to get:
\n" ); document.write( "3 * p - 2 * q = -2
\n" ); document.write( "your two equations are now:
\n" ); document.write( "-2 * p + 3 * q = 13
\n" ); document.write( "3 * p - 2 * q = -2
\n" ); document.write( "multiply both sides of the firest equation by 3 and multiply both sides of the second equation by 2 to get:
\n" ); document.write( "-6 * p + 9 * q = 39
\n" ); document.write( "6 * p - 4 * q = -4
\n" ); document.write( "add the two equations together to get:
\n" ); document.write( "5 * q = 35
\n" ); document.write( "solve for q to get:
\n" ); document.write( "q = 7
\n" ); document.write( "replace q with 7 in the first equation to get:
\n" ); document.write( "-6 * p + 9 * 7 = 39
\n" ); document.write( "simplify to get:
\n" ); document.write( "-6 * p + 63 = 39
\n" ); document.write( "subtract 63 from both sides to get:
\n" ); document.write( "-6 * p = -24
\n" ); document.write( "divide both sides by -6 to get:
\n" ); document.write( "p = 4
\n" ); document.write( "your values for p and q are now:
\n" ); document.write( "p = 4
\n" ); document.write( "q = 7
\n" ); document.write( "go back to the two equations of:
\n" ); document.write( "-2 * p + 3 * q = 13
\n" ); document.write( "-2 * q + 3 * (p + 1) = 1
\n" ); document.write( "replace p with 4 and q with 7 to get:
\n" ); document.write( "-2 * 4 + 3 * 7 = 13 becomes -8 + 21 = 13 which becomes 13 = 13.
\n" ); document.write( "-2 * 7 + 3 * (4 + 1) becomes -14 + 15 = 1 which becomes 1 = 1.
\n" ); document.write( "this confirms the values of p and q are correct.
\n" ); document.write( "your solution is that the values of p and q are 4 and 7, respectively.\r
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