document.write( "Question 103246: Hello out there,I need some help with some problems,the first one is,Use substitution to solve:x=3y-2 and 2x+4y=16.The next one is,Use substitution to solve:2x+y=7 and 5x-2y=4.The third one is,Find the solution of the system,y=x^2+5 and y=2x+4.And the last one is,Solve the system of equations by graphing:y=x^2-4 and y=x-2.Thanks to whoever can help. \n" ); document.write( "
Algebra.Com's Answer #75187 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Use substitution to solve:
\n" ); document.write( "x = 3y - 2
\n" ); document.write( "2x + 4y = 16.
\n" ); document.write( "Substitute (3y-2) for x in the second equation, solve for y
\n" ); document.write( "2(3y-2) + 4y = 16
\n" ); document.write( "6y - 4 + 4y = 16
\n" ); document.write( "6y + 4y = 16 + 4
\n" ); document.write( "10y = 20
\n" ); document.write( "y = 20/10
\n" ); document.write( "y = 2
\n" ); document.write( "Find x substitute 2 for y
\n" ); document.write( "x = 3(2) - 2
\n" ); document.write( "x = 6 - 2
\n" ); document.write( "x = 4
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Use substitution to solve:
\n" ); document.write( "2x + y = 7
\n" ); document.write( "y = (7 - 2x); we can substitute (7-2x) for y in the next equation, find x
\n" ); document.write( "5x - 2y = 4
\n" ); document.write( "5x - 2(7-2x) = 4
\n" ); document.write( "5x - 14 + 4x = 4; remember a neg outside the brackets changes the signs inside
\n" ); document.write( "5x + 4x = 4 + 14
\n" ); document.write( "9x = 18
\n" ); document.write( "x = 18/2
\n" ); document.write( "x = 2
\n" ); document.write( "Find y using y = (7-2x)
\n" ); document.write( "y = 7 - 2(2)
\n" ); document.write( "y = 7 - 4
\n" ); document.write( "y = 3
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Find the solution of the system,
\n" ); document.write( "y = x^2 + 5
\n" ); document.write( "y = 2x + 4
\n" ); document.write( "Substitute (x^2 + 5) from the 1st equation, for y in the 2nd equation:
\n" ); document.write( "x^2 + 5 = 2x + 4
\n" ); document.write( "x^2 - 2x + 5 - 4 = 0
\n" ); document.write( "x^2 - 2x + 1; a quadratic equation that we can factor to:
\n" ); document.write( "(x-1)(x-1)
\n" ); document.write( "x = 1
\n" ); document.write( "Find y using the 2nd equation:
\n" ); document.write( "y = 2(1) + 4
\n" ); document.write( "y = 2 + 4
\n" ); document.write( "y = 6
\n" ); document.write( "Check it by substitution in the 1st equation
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Solve the system of equations by graphing:
\n" ); document.write( "y = x^2 - 4
\n" ); document.write( "y = x - 2
\n" ); document.write( "Plot these. substitute for x = -3 to x = +3
\n" ); document.write( "The first equation table
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( "-3 | +5
\n" ); document.write( "-2 | 0
\n" ); document.write( "-1 | -3
\n" ); document.write( " 0 | -4
\n" ); document.write( "+1 | -3
\n" ); document.write( "+2 | 0
\n" ); document.write( "+3 | +5
\n" ); document.write( "Note that this is a parabola
\n" ); document.write( ":
\n" ); document.write( "The 2nd equation is linear, two points are sufficient
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( "-3 |-5
\n" ); document.write( "+3 |+1
\n" ); document.write( ":
\n" ); document.write( "The graph should look like this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+6%2C+-6%2C+6%2C+x%5E2-4%2C+x-2%29+\"
\n" ); document.write( ":
\n" ); document.write( "There are two solutions, where the two graphs intersect. I'll let you figure
\n" ); document.write( "out what they are from the graph. When you have decided what they are, check
\n" ); document.write( "by substitution in the original equations. \n" ); document.write( "
\n" );