Question 58851This question is from textbook Beginning Algebra
: Could someone be so kind in helping me with this problem?
I need to solve the following systems by substitution:
8x - 4y = 16
y = 2x - 4
Thank you so much,
Ashley
This question is from textbook Beginning Algebra
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Hi Ashley,
Solve the following systems by substitution:
L1) 8x - 4y = 16
L2) y = 2x - 4
Substitute 2x-4 for y in L2) and solve for x:
8x-4(2x-4)=16
8x-8x-16=16
0+16=16
16=16
Your variable was eliminated and 16 = 16, therefore there is an infinite number of solutions. The lines are lying on top of each other, they are graphically the same line and have all points in common.
Some books list the solution to something with an infinite number of solutions as (x,2x-4). Most are happy with "all real numbers" or "infinite solutions."
:
Just to prove a point, watch what happens when you try to solve L1 for y:
8x-4y=16
-8x+8x-4y=-8x+16
-4y=-8x+16
-4y/-4=-8x/-4+16/-4
y=2x-4 It turns right into L2!
Happy Calculating!!!
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