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Question 78208: Solve the system y=2x+3 and y=4x+7 using the substitution method.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given: The equation set y = 2x + 3 and y = 4x + 7
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You are asked to solve this set by substitution. Note that the first equation defines
the value of y in terms of x. Therefore, you can use the right side of this equation
(2x + 3) as a substitution for y in the second equation. When you substitute 2x +3 for y
in the second equation, the result is:
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2x + 3 = 4x + 7
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Let's set the goal of getting all the terms that contain x isolated on the left side of
the equal sign and all the constants by themselves on the right side. Begin by getting rid
of the +3 on the left side by subtracting 3 from the left side. But if you subtract
3 from the left side you must also subtract 3 from the right side. These subtractions
result in the following sequence:
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2x + 3 - 3 = 4x + 7 - 3
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Combining numbers on the left side and on the right side simplifies the equation to:
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2x = 4x + 4
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Now, in a similar fashion, let's get rid of the 4x on the right side by subtracting
4x from the right side. When we do this subtraction, to keep the equation in balance
we must also subtract 4x from the left side. This results in:
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2x - 4x = 4x - 4x + 4
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On both sides of the equation combine terms containing x to get:
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-2x = 4
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Finally, solve for x by dividing both sides of the equation by -2 because -2 is the multiplier
of x. This results in:
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x = 4/-2 = -2
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So now that we know x = -2, we can return to either one of the original equations
in the equation set and substitute -2 for x. Then we can solve for y. Let's return
to the first equation and substitute -2 for x. This begins with:
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y = 2x + 3
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Then substituting -2 for x gives:
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y = 2*(-2) + 3 = -4 + 3 = -1
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In summary, our answers for the equation set is x = -2 and y = -1. Keep in mind what this
means ... both equations are satisfied by setting x to -2 and y to -1. It also means that
the point (-2,-1) is the point at which the graphs of the two equations intersect.
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Hope this helps you to understand how to solve for the variables in the equation set by
using the process of substitution.
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