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      Carl y Cody              using graphing the first step we took was to change the both the equations to the same form. So, we changed both problems to slope-intercept form. for example the equation 2x+y=4 turns into y=-2x+4. Then you put the first point at -1 and then you go up one over two and put the next point and keep going up one over one. For the next line you put the first point at 4 and then you go up 1 over 2

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      Carl y Cody              using graphing the first step we took was to change the both the equations to the same form. So, we changed both problems to slope-intercept form. for example the equation 2x+y=4 turns into y=-2x+4. Then you put the first point at -1 and then you go up one over two and put the next point and keep going up one over one. For the next line you put the first point at 4 and then you go up 1 over 2

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Part D:
We first took the first bee´s path and started at y=4. Then, we went down 2, over to the right 1 until we hit the x-axis. Afterward, we took the second bee´s path and started at y=-1. Then, we went up 1, over to the right 2 until we hit the x-axis again. The bee hive was at (2 , 0), where the bees meet.

Part E:
We used substitution to prove our answer. First, we took 1/2x-1 and plugged it into 2x+y=4, the result was 2x+1/2x-1=4. If you evaluate the equation, the answer will be x=2. Then, we took x=2 and plugged it back into y=1/2x-1, the result was y=1/2(2)-1. If you evaluate the equation, the answer will be y=0. This proves that the solution to the system is (2 , 0)

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Put the equation in slope intercept form.  Then you graph 4 on the y int. Then you graph the slope. Do the same for the other equation. (2,o)

-2x+4=1/2x-1
+2x___+2x___
4+2 1/2x-1
+1_______+1
2 1/2x=5
---------    ------
2 1/2     2 1/2
x=2
Plug it in

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First, we changed the equation 2x+y=4  into slope-intercept form, which changed into y=-2x+4. We then graphed the two equations, which intercepted on the point (2,0)

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first you had to put the equation in slope intercept form, them you graph it and find were the point intersect.

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Joshua Baucom, Thomas Coder, and Cope Brewer

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Joshua Baucom, Thomas Coder, and Cope Brewer

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I graphed it by using the 2 equations and putting one in slope intercept form, then just recorded the points

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We first made the equations in slope intercept form. Because that made it easy to plot the points of the yInterxept  whixh was 4 and negative 1. The you follow the points of the slope and they meet @ (2,0)

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We started by changing the equation into slope intercept form ( y= -2x + 4).  We then graphed to get the solution (2,0).

Substitution : Use substitution to substitute, 1/2x into 2x+y=4. Solve. Then  plug in answer for x. Solve, to get solution (2,0).

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First, change the equation 2x+y=4 into slope-intercept form by subtracting 2x on both sides of the equaion. This will equal y=-2x+4.
Then, plot the y intercept of the first equation on the graph (4). Since the slope is -2, you have to go down 2 and over 1. After that, graph the second equation. Plot the y intercept on the same graph and go up 1 over 2. Both lines will intersect at (2,0). This is your solution.

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First we had to change the equation to slope intercept, then put our first point on y line ad positive 4 then went down 2 over 1 to the right. Next we drew our line down. After we put our point at negative 1 and went up 1 over to the right 2 times and drew our line. Last we found the point that both of the lines met at and it was (2,0). For substitution, we plugged in 1/2x-1 into 2x+y=4. We got 2x+1/2x-1. We simplified it to 5/2x-1=4. Add 1 to 4 then to get x by itself, we multiplied 2/5 to both sides. 5 times 2/5 equals 2. Plug 2 back in for x to get y. 1/2(2)-1=0. 1-1 =0. Y is 0. (2,0).

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Ashton and Karissa

First we had to change 2x+y=4 into y-intercept form which was y=-2x+4. Now scene they both equal y, make them equal each other ( 1/2x -1=-2x=4). Then solve for x to get 2. After that substitute 2 for x in ONE of the equations, solve for y. Then your answer is (2,0). When you graph, put equations  in y-intercept form. Graph both equations and the solution is the only point the two lines intersect which is (2,0).

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using substitution to solve our problem, we first changed each equation into slope intercept form. Then we took the equation y=1/2x - 1 and substituted it for y in the equation 2x+y=4 . You're new equation would be 2x+1/2x - 1 = 4. You combine the X's to get 2.5x-1=4, then add 1 to each side to get 2.5x=5. Next you divide 2.5 from 5 to get X=2. then replace X in the equation 2x+y=4 with 2 to get 2(2)+y=4 . You  get 4+y=4, subtract 4 and you get y=0. So your solution to the equation in (2, 0).

using graphing to solve our problem, you first change each equation into slope intercept form. then take the equation Y=1/2x-1 and graph it by putting a point at -1 and going up 1 over 2 each time. then take the equation y=-2x+4 and put point at positive 4 then go down 2 over 1. those two equation meet at (2, 0).

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Give a detailed explanation of how you arrived at your solution to the system (hive) using graphing & either substitution or elimination