SOLUTION: Trying to check my daughter's homework, not sure I remember how. Q. Solve by graphing: y=-x+2 & 3x+3y=12 A. She has 12 = -3x+3y & (0,2) as answers and a graph that does

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Question 398222: Trying to check my daughter's homework, not sure I remember how.
Q. Solve by graphing: y=-x+2 & 3x+3y=12
A. She has 12 = -3x+3y & (0,2) as answers and a graph that doesn't look right to me.
If you can walk me through this prob., I can prob. help her on the others.
Thanks in advance for your help!

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Q. Solve by graphing: y=-x+2 & 3x+3y=12
A. She has 12 = -3x+3y & (0,2) as answers and a graph that doesn't look right to me.
--------------------
You can check that answer by letting x = 0 and y = 2
in the two sentences.
You would get:
2 = 0+2 which is ok
You would also get:
3*0+3*2 = 12
0+6 = 12
6 = 12 which is not ok
---------------------------
Graph each equation by plotting 2 points and drawing a line thru them.
y = -x+2
Let x = 0, then y = 2 giving you point (0,2)
Let x = 1, then y = -1+2 = 1 giving you point (1,1)
===========================
3x+3y=12
Let x = 0, then 3y= 12, and y = 4 giving you point (0,4)
Let x = 2, then 3*2+3y=12 and 3y = 6 so y = 2 giving you point (2,2)
------------------------------

---
Do you see there is no solution because the lines are parallel.
==================
Cheers,
Stan H.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
y=-x+2

get some points for the line y = -x+2

 x | y
 0 | 
-1 | 
 4 |

x=0            x=-1              x=4
y = -x+2       y = -x+2          y = -x+2
y = -0+2       y = = -(-1)+2     y = -(4)+2
y = 2          y = +1+2          y = -4+2 
               y = 3             y = -2

 x | y
 0 | 2
-1 | 3
 4 |-2

Plot those points and connect them:



Now get some points for the other line 3x+3y=12

 x | y
 0 |  
-1 | 
 4 |

  x=0             x=-1             x=4
  3x+3y=12        3x+3y=12         3x+3y=12
3(0)+3y=12     3(-1)+3y=12       3(4)+3y=12
   0+3y=12      -3 + 3y=12         12+3y=12 
     3y=12           3y=15            3y= 0
      y=4             y= 5             y= 0



 x | y
 0 | 4
-1 | 5
 4 | 0

Plot those points and connect them:



 
The lines do not intersect since they are parallel, so
there is no solution.

Edwin
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