document.write( "Question 888995: I am stuck on this equation -2x+y-3=0, 4x+y+3=0 . The answer is -1,1 but I do not see how they get it. \n" ); document.write( "
Algebra.Com's Answer #537820 by algebrapro18(249)\"\" \"About 
You can put this solution on YOUR website!
There are actually 3 ways to solve this problem. You can either solve the system by graphing, substitution, or elimination. I will show you how to do all 3.
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    1)Solve by graphing

\n" ); document.write( "Steps for solving a system of equation graphically:
\n" ); document.write( " 1)Get the first equation into y=mx+b form(solve for y)
\n" ); document.write( " 2)Find your M and B(M=slope and B = Y-intercept) *Remember your slope = your change in the y direction/your change in the x direction*
\n" ); document.write( " 3)Use your B and M to find two points on the line. These points will be (0,B) and (0+Change in x,B+Change in y).
\n" ); document.write( " 4)Get the second equation into y=mx+b form(solve for y)
\n" ); document.write( " 5)Find your M and B(M=slope and B = Y-intercept)
\n" ); document.write( " 6)Use your B and M to find two points on the line. These points will be (0,B) and (0+Change in x,B+Change in y).
\n" ); document.write( " 7)Graph the lines(plot the points from 3 and connect them and plot the points from 6 and connect them)
\n" ); document.write( " 8) Find the point where the two lines intersect.
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\n" ); document.write( "\n" ); document.write( "1)Solving the first equation for y we get:
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\n" ); document.write( "\n" ); document.write( "-2x+y-3=0 Add 3 to both sides
\n" ); document.write( "-2x+y=3 Add 2x to both sides
\n" ); document.write( "y = 3+2x = 2x+3
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\n" ); document.write( "\n" ); document.write( "2)M = 2/1 and B = 3
\n" ); document.write( "3)Remembering that slope is change in y over change in x we get our points to be (0,B) and (0+Change in x,B+Change in y) or (0,3) and (0+1,3+2) or (0,3) and (1,5).
\n" ); document.write( "4)Solving the second equation for y we get:
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\n" ); document.write( "\n" ); document.write( "4x+y+3=0 Subtract 3 from both sides
\n" ); document.write( "4x+y = -3 Subtract x from both sides
\n" ); document.write( "y=-4x-3
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\n" ); document.write( "\n" ); document.write( "5)M=-4/1 and B = -3
\n" ); document.write( "6)Remembering that slope is change in y over change in x we get our points to be (0,B) and (0+Change in x,B+Change in y) or (0,-3) and (0+1,-3+-4) or (0,-3) and (1,-7).
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\n" ); document.write( "\n" ); document.write( "7)Graphing the points you get the following graph:
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\n" ); document.write( "\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%2B3%2C+-4x-3%29+\"
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\n" ); document.write( "\n" ); document.write( "8) Looking at the graph you can see that the lines intersect at (-1,1).
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    2)Solve by Substitution

\n" ); document.write( "Steps for solving systems using the Substitution method:
\n" ); document.write( " 1)Solve one of the equations for either x or y
\n" ); document.write( " 2)Plug that expression into the other equation and solve for either x or y(which ever one you didn't solve for in step 1)
\n" ); document.write( " 3)Plug your solution from 2 into the expression in step 1 and solve for the varable.\r
\n" ); document.write( "\n" ); document.write( "1) We can solve the first equation for y(which we did above). This will give us the expression \"y=2x%2B3\".
\n" ); document.write( "2) We can plug 2x+3 into the second equation for y and solve for x.
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\n" ); document.write( "\n" ); document.write( "4x+y+3 = 0 Substitute 2x+3 in for y
\n" ); document.write( "4x+2x+3+3=0 Combine like terms
\n" ); document.write( "6x+6 = 0 Subtract 6 from both sides
\n" ); document.write( "6x = -6 Divide both sides by 6
\n" ); document.write( "x = -1
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\n" ); document.write( "\n" ); document.write( "3)Now we now that x = -1 we can plug that into \"y=2x%2B3\" and solve for y.
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\n" ); document.write( "\n" ); document.write( "y=2x+3 Plug -1 in for x
\n" ); document.write( "y=2(-1)+3 Multiply
\n" ); document.write( "y=-2+3 Add
\n" ); document.write( "y=1
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\n" ); document.write( "\n" ); document.write( "So we get the answer (-1,1) which is the same answer we got when we graphed it.\r
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    3)Solve by Elimination

\n" ); document.write( "Steps for Solving a system by the elimination method:
\n" ); document.write( "1)Manipulate your two equations such that when you add them together one of the variables drop out.
\n" ); document.write( "2)Add the new equations together.
\n" ); document.write( "3) Solve the resulting equation for the remaining variable.
\n" ); document.write( "4) Plug in that solution into either of the original equations and solve for the eliminated variable.\r
\n" ); document.write( "\n" ); document.write( "1)If we multiply the first equation by 2 it will make the x's drop out if we add the two equations together.
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\n" ); document.write( "\n" ); document.write( "2(-2x+y-3=0)
\n" ); document.write( "-4x+2y-6 = 0
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\n" ); document.write( "\n" ); document.write( "2) Adding the two equations together we get:

\n" ); document.write( "-4x+2y-6 = 0
\n" ); document.write( "+4x+y+3 = 0
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\n" ); document.write( "3y-3=0
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\n" ); document.write( "\n" ); document.write( "3) Solving for y we get:
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\n" ); document.write( "\n" ); document.write( "3y-3=0 Add 3 to both sides
\n" ); document.write( "3y = 3 Divide both sides by 3
\n" ); document.write( "y = 1
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\n" ); document.write( "\n" ); document.write( "4) Plugging y=1 into the bottom equation and solving for x we get:
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\n" ); document.write( "\n" ); document.write( "4x+y+3=0
\n" ); document.write( "4x+(1)+3=0
\n" ); document.write( "4x+4=0
\n" ); document.write( "4x=-4
\n" ); document.write( "x=-1
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\n" ); document.write( "\n" ); document.write( "So either of the 3 ways yield the same solution of (-1,1). \n" ); document.write( "
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