You can put this solution on YOUR website! solution
-8x+2y=8
take -8x over the equality
2y=8+8x
now bring out the like terms on the left side
2y=8(1+x)
divide both sides by 2
y=4(1+x)
expand the bracket
y=4+4x
You can put this solution on YOUR website! Given the equation set:
.
–8x + 2y = 8
y = 4 + 4x
.
Solve by addition or substitution.
.
First by addition:
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Rearrange the bottom equation so that it is in the same arrangement as the top equation.
So get the bottom equation so the terms containing x and y are on the left side and the
constants are on the right side. Do it using the following process:
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y = 4 + 4x
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eliminate the 4x on the right side by subtracting 4x from both sides to get:
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-4x + y = 4
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This is in the form of the original top equation. So now the equation set is:
.
-8x + 2y = 8
-4x + y = 0
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If you now multiply both sides of the bottom equation by -2 the equation set becomes:
.
-8x + 2y = 8
+8x - 2y = 0
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Now you can add the two equations. But notice that when you do that the result is that
both the x and the y terms on the left side cancel each other and the result is:
.
0 = 0
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More significantly, look at what we did to the bottom equation. We rearranged it and then
multiplied both sides by a common number. Suppose that instead of multiplying the rearranged
bottom equation by -2 we had multiplied it by +2. The result would have been that it
would become -8x + 2y = 8 and the equation set would then be:
.
-8x + 2y = 8 and
-8x + 2y = 8
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This shows that the bottom equation is actually the same as the top equation. And that
means that any solution of the top equation is also a solution to the bottom equation.
So for the given set of equations, there are an infinite number of common solutions,
not just one. Any solution for one of the equations is common with the other equation
because both equations are the same.
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If you try to solve this by substitution, you can notice that the original bottom
equation is already solved for y. So you can substitute the right side of the bottom
equation for y in the top equation. When you do that substitution the top equation
becomes:
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-8x + 2(4 + 4x) = 8
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Do the distributed multiplication on the left side by multiplying 2 times each of the
terms in parentheses to get:
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-8x + 8 + 8x = 8
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Notice again how the two terms containing x cancel and the equation becomes:
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8 = 8
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And subtracting 8 from both sides again results in 0 = 0. This again is a clue that something
is amiss and that the two equations have to be identical for both sides to become
0 = 0. Again the conclusion is that if the equations are identical (or can be made so
with some permissible algebraic manipulations) then every solution of one is a solution
of the other ... and there are an infinite number of common solutions.
.
Hope this helps you to understand this "tricky" problem.
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