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subtitution and Elimination #3b

1)  y=-5x+2
     y=3x-14
 
2)  x+y=0
     5x+y=4

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Randy B. | Algebra, Prealgebra, Precalculus, Geometry, Mathematics, ReadingAlgebra, Prealgebra, Precalculus, Geomet...
4.8 4.8 (13 lesson ratings) (13)
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Andrea, 
 
 
    Jason's answers are good.  :)  
 
Randy B.
 
PS   If you will go to this website and work through the section on Systems of Equations, you will learn, understand, and soon be helping everybody in your class.  
 
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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1)
 
y = -5x + 2
y = 3x - 14
 
Set them both equal to each other since both are equal to y.
 
-5x + 2 = 3x - 14
+5x         +5x
 
2 = 8x -14
+14    +14
 
16 = 8x
 
x = 2  
 
y = 3(2)- 14 = -8
 
 
2)
x+y=0
5x+y=4
---------
Multiply the top by -1
 
-x - y = 0
5x + y = 4
 
Add the two equations.
 
5x-x = 4x, y - y = 0, 4 + 0 = 4 
4x = 4
x = 1
 
5(1) + y = 4
5 + y = 4
-5        -5
 
y = -1
 

Comments

Hi Jason.  thanks for your answers, but I don't understand #2 at all.  Why multiply by -1,and what do you multiply?   then I don't know how you even got the equations.   Please explain.
You multiply the top equation by -1 so that the y's will sum to 0 (cancel out) when you add the two equations together.
 
x + y = 0
5x + y = 4
 
(-1)(x) + (-1)(y) = (-1)(0)
 
    -x - y     =    0
+ (5x + y)  = + 4
---------------------
 
5x-1x = 4x
y-y = 0
4+0  = 4
 
So
4x + 0  = 4
4x = 4
 
Divide both sides by 4.
 
4x/4 = 4/4
 
x = 1
 
Now plug 1 in for x:
x + y = 0
 
1 + y = 0
 
Subtract 1 from both sides:
 
1 + y -1 = 0-1
y = -1
 
Thanks again!  Jason, having a real hard time using the method I now know with this last one, can you help? I've been at it for about an hour now. 
-1/2x-1/4y=3
1/3x+1/6y=2
 
Multiply the top equation by 4 and the bottom by 6.
 
-2x - y = 12
2x + y = 12
 
Add them together and you get:
 
0 = 24.  This is always false.
 
Therefore, no solution is possible.
 
Note also that if you change them to y = mx+b format:
y = -2x - 12
y = -2x + 12
 
Since the slopes are the same, they are parallel and never intersect.  Thus, the "No solution" answer is correct.
 
Have a great day.