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.
Found 2 solutions by richwmiller, algebrapro18:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! first rearrange it
-2x+y=3,
4x+y=-3
-2,1,3
4,1,-3
divide row 1 by -2/1
1,1/-2,3/-2
4,1,-3
add down (-4/1) *row 1 to row 2
1,1/-2,3/-2
0,3,3
divide row 2 by 3/1
1,1/-2,3/-2
0,1,1
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-1/-2) *row 2 to row 1
1,0,-1
0,1,1
final
1,0,-1
0,1,1
x=-1
y=1
Answer by algebrapro18(249)  (Show Source):
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.
Steps for solving a system of equation graphically:
1)Get the first equation into y=mx+b form(solve for y)
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*
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).
4)Get the second equation into y=mx+b form(solve for y)
5)Find your M and B(M=slope and B = Y-intercept)
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).
7)Graph the lines(plot the points from 3 and connect them and plot the points from 6 and connect them)
8) Find the point where the two lines intersect.
1)Solving the first equation for y we get:
-2x+y-3=0 Add 3 to both sides
-2x+y=3 Add 2x to both sides
y = 3+2x = 2x+3
2)M = 2/1 and B = 3
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).
4)Solving the second equation for y we get:
4x+y+3=0 Subtract 3 from both sides
4x+y = -3 Subtract x from both sides
y=-4x-3
5)M=-4/1 and B = -3
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).
7)Graphing the points you get the following graph:
8) Looking at the graph you can see that the lines intersect at (-1,1).
Steps for solving systems using the Substitution method:
1)Solve one of the equations for either x or y
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)
3)Plug your solution from 2 into the expression in step 1 and solve for the varable.
1) We can solve the first equation for y(which we did above). This will give us the expression  .
2) We can plug 2x+3 into the second equation for y and solve for x.
4x+y+3 = 0 Substitute 2x+3 in for y
4x+2x+3+3=0 Combine like terms
6x+6 = 0 Subtract 6 from both sides
6x = -6 Divide both sides by 6
x = -1
3)Now we now that x = -1 we can plug that into and solve for y.
y=2x+3 Plug -1 in for x
y=2(-1)+3 Multiply
y=-2+3 Add
y=1
So we get the answer (-1,1) which is the same answer we got when we graphed it.
Steps for Solving a system by the elimination method:
1)Manipulate your two equations such that when you add them together one of the variables drop out.
2)Add the new equations together.
3) Solve the resulting equation for the remaining variable.
4) Plug in that solution into either of the original equations and solve for the eliminated variable.
1)If we multiply the first equation by 2 it will make the x's drop out if we add the two equations together.
2(-2x+y-3=0)
-4x+2y-6 = 0
2) Adding the two equations together we get:
-4x+2y-6 = 0
+4x+y+3 = 0
--------------
3y-3=0
3) Solving for y we get:
3y-3=0 Add 3 to both sides
3y = 3 Divide both sides by 3
y = 1
4) Plugging y=1 into the bottom equation and solving for x we get:
4x+y+3=0
4x+(1)+3=0
4x+4=0
4x=-4
x=-1
So either of the 3 ways yield the same solution of (-1,1).
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