document.write( "Question 386322: I need help to show me how to work out the use the substitution to solve the equations and state if it has no solution or infinitely many solutions: 2x+7y=3 x=1-4y \n" ); document.write( "

Algebra.Com's Answer #273108 by Earlsdon(6294) $\"\"$ $\"About$

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Solve by substitution:
\n" ); document.write( " $\"2x%2B7y+=+3\"$
\n" ); document.write( " $\"x+=+1-4y\"$ Substitute this x into the first equation then solve for y.
\n" ); document.write( " $\"2%281-4y%29%2B7y+=+3\"$ Simplify.
\n" ); document.write( " $\"2-8y%2B7y+=+3\"$
\n" ); document.write( " $\"2-y+=+3\"$ Subtract 2 from both sides.
\n" ); document.write( " $\"-y+=+1\"$ Multiply by -1 to make y positive.
\n" ); document.write( " $\"y+=+-1\"$ Now substitute this value of y into either one of the two given equations and solve for x. Let's use the second equation.
\n" ); document.write( " $\"x+=+1-4y\"$ Substitute $\"y+=+-1\"$
\n" ); document.write( " $\"x+=+1-4%28-1%29\"$ Simplify.
\n" ); document.write( " $\"x+=+1%2B4\"$
\n" ); document.write( " $\"x+=+5\"$
\n" ); document.write( "The solution is: (5, -1)
\n" ); document.write( "Let's look at the graphic solution:
\n" ); document.write( " $\"graph%28400%2C400%2C-2%2C10%2C-2%2C1%2C-%282%2F7%29x%2B3%2F7%2C-%281%2F4%29x%2B1%2F4%29\"$
\n" ); document.write( "The solution is where the two lines intersect (5, -1) \n" ); document.write( "

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