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First lets let y equal one number and x equal the other unknown number. We need to come up with equations involving x and y. The first sentence as an equation looks like y = 4x-5. The other equation would be xy=21. So now we have a system of equations that we can solve. I'm going to solve it using substitution. The system is as follows:
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\n" ); document.write( "\n" ); document.write( "y= 4x-5
\n" ); document.write( "xy = 21
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\n" ); document.write( "\n" ); document.write( "Substituting y = 5-4x into the second equation we get:
\n" ); document.write( "xy=21
\n" ); document.write( "x(4x-5)=21
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\n" ); document.write( "\n" ); document.write( "Now we can solve that equation for x:
\n" ); document.write( "x(4x-5) Distribute
\n" ); document.write( "4x^2-5x=21 Subtract 21 from both sides
\n" ); document.write( "4x^2-5x-21 = 0 Factoring the left hand side
\n" ); document.write( "(4x+7)(x-3)=0 Set each factor equal to 0
\n" ); document.write( "4x+7 = 0 and x-3 = 0
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\n" ); document.write( "\n" ); document.write( "Solving 4x+7=0:
\n" ); document.write( "4x+7=0 Subtract 7 from both sides
\n" ); document.write( "4x=-7 Divide both sides by 4
\n" ); document.write( "x=-7/4
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\n" ); document.write( "\n" ); document.write( "Since the question specified that both numbers are integers we know that x can not be -7/4th so we eliminate this solution.
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\n" ); document.write( "\n" ); document.write( "Solving x-3=0:
\n" ); document.write( "x-3=0 add 3 to both sides
\n" ); document.write( "x = 3
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\n" ); document.write( "\n" ); document.write( "Now we can Plug x = 3 into the first equation(y=4x-5) and solve for y:
\n" ); document.write( "y=4x-5 Plug in x = 3
\n" ); document.write( "y=4(3)-5 Simplify
\n" ); document.write( "y = 12-5 Simplify
\n" ); document.write( "y = 7
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\n" ); document.write( "\n" ); document.write( "Checking our work we see that 7 is 5 less than 4 times 3 and that 7*3 is 21. \n" ); document.write( "