SOLUTION: Solve each of the following systems by substitution. 16. 5x -2y = -5 y-5x = 3 20. 8x -4y = 16 y= 2x -4 28.) 4x -12y = 5 -x + 3y= -1

Algebra ->  Linear-equations -> SOLUTION: Solve each of the following systems by substitution. 16. 5x -2y = -5 y-5x = 3 20. 8x -4y = 16 y= 2x -4 28.) 4x -12y = 5 -x + 3y= -1       Log On


   



Question 100424: Solve each of the following systems by substitution.
16. 5x -2y = -5
y-5x = 3
20. 8x -4y = 16
y= 2x -4
28.) 4x -12y = 5
-x + 3y= -1

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
16)
5X-2Y=-5
-5X+Y=3 NOW ADD
--------------------------
-Y=-2
Y=2 NOW REPLACE Y WITH 2 & SOLVE FOR X
5X-2*2=-5
5X-4=-5
5X=-5+4
5X=-1
X=-1/5
--------------------------------------------
20)
8X-4Y=16 NOW MULTIPLY THE OTHER EQUATION BY 4 OR (-8Y+4Y=-16) & ADD THEM:
-8X+4Y=-16
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28)
4X-12Y=5 NOW MULTIPLY THE SECOND EQUATION BY 4 & ADD:
-4X+12Y=-4
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0+0=1 AGAIN NO UNIQUE SOLUTION.
0=0 THIS SAYS THAT THESE TWO EQUATIONS ARE THE SAME. THEREFORE THERE IS NO UNIQUE SOLUTION WITH ONE EQUATION & TWO UNKNOWNS.
CONVERTING THESE EQUATUIONS TO LINE EQUATIONS WE'LL SEE THAT THEY NEVER INTERSECT:
4x-12y=5 or -12y=-4x+5 or y=-4x/-12+5/-12 or y=x/3-5/12 (red line)
-x+3y=-1 or 3y=x-1 or y=x/3-1 (green line)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+x%2F3+-5%2F12%2C+y+=+x%2F3+-1%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = 3x -5/12 and y= x/3 -1).
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