document.write( "Question 182290: Write a system of two equations in two unknown for each problem. Solve each system by substitution. The sum of two numbers is –16 and their difference is 8. Find the numbers \n" ); document.write( "

Algebra.Com's Answer #136820 by MathGuyJoe(20) $\"\"$ $\"About$

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First Equation
\n" ); document.write( "\"The sum of two numbers is -16\":
\n" ); document.write( "x + y = -16
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\n" ); document.write( "\"Their difference is 8\":
\n" ); document.write( "x - y = 8
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\n" ); document.write( "To solve by substitution, we take one equation and solve for one of the numbers (in terms of the other) -- let's solve the second equation for x (in terms of y). To do this we add \"y\" to both sides:
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document.write( "x - y (+ y) = 8 (+ y)
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document.write( "x = 8 + y
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\n" ); document.write( "Next we substitute \"8 + y\" into the first equation, for \"x\" and solve for \"y\":
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document.write( "(8 + y) + y = -16
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document.write( "8 + 2y = -16
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document.write( "2y = -24
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document.write( "y = -12
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\n" ); document.write( "Now that we know y is -12, we can substitute that value into either equation to find x -- let's substitute it into the first equation and solve for \"x\":
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document.write( "x + (-12) = -16
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document.write( "x = -4
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\n" ); document.write( "So our two numbers are -4 and -12. \n" ); document.write( "

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