Question 90077: Solve by substitution. Please help.
8x-4y = 16
y = 2x -4
Thanks in advance.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the two equations:
.
8x-4y = 16
y = 2x -4
.
The problem is to solve them by substitution.
.
Note that the second equation already tells us the value for y. It says that y is equal
to 2x - 4.
.
Therefore, we can go to the first equation and substitute 2x - 4 for y. When you do that
the first equation is transformed to:
.
8x - 4(2x - 4) = 16
.
Multiply out the left side by multiplying -4 times each of the terms in the parentheses to
get:
.
8x - 8x + 16 = 16
.
Ooops. We know that something is wrong because the 8x and - 8x cancel each other and the
equation is reduced to 16 = 16.
.
We need to go back to the original set of equations and see what the problem might be.
.
The original set of equations is:
.
8x-4y = 16
y = 2x -4
.
Let's multiply the second equation (both sides, all terms) by -4. When you do that the equation
becomes:
.
-4y = -8x + 16
.
Next let's get it into the form of the first equation by adding 8x to both sides.
When you do that the second equation becomes:
.
8x - 4y = 16
.
This means that the second equation is identical to the first equation. Therefore, every
solution to the first equation is also a solution to the second equation also. And if you
graphed both equations, the graphs would lie on top of each other. The equations have no
singular solution ... every solution to one is a solution to the other also.
.
Hope this helps to explain the difficulty you encountered in solving this set of equations.
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