Question 127524: y=-3x+4
y=x-4 how do u do that?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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y = -3x + 4 and
y = +x - 4
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One way you can do this problem is to recognize that each of the two equations has y as its
left side. For the two left sides to be equal, (y = y in both equations) then the two right
sides must also be equal. If the two right sides are equal, then we can set them equal in
the form of an equation as follows:
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-3x + 4 = x - 4
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[Note that this follows the algebraic rule that if two quantities are equal to the same quantity
then the two quantities must also be equal. Both the right sides are equal to y so these two
right sides must also be equal to each other.]
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Get rid of the +4 on the left side by subtracting 4 from both sides. When you do that subtraction
the equation becomes:
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-3x = x - 8
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Next, get rid of the x on the right side by subtracting x from both sides to change the
equation to:
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-3x - x = -8
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Combine the two terms on the left side and you have:
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-4x = -8
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Solve for x by dividing both sides by -4 and the equation becomes:
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x = -8/-4 = +2
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Then you can solve for y by returning to either of the 2 original equations and substituting +2
for x. Let's return to the equation y = x - 4 and calculate the corresponding value of
y.
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y = x - 4
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Substitute +2 for x and the equation becomes:
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y = 2 - 4 = -2
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So the common solution becomes x = 2 and y = -2 or (+2, -2) in point form.
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Let's return to the other original equation and see if y = -2 and x = +2 are a common solution.
We start with:
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y = -3x + 4
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Substitute -2 for y and +2 for x to get:
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-2 = -3(2) + 4
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Do the multiplication on the right side by multiplying -3 times 2 to get:
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-2 = -6 + 4
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If you combine the two terms on the right side the equation becomes:
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-2 = -2
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And since this is true we know that y = -2 and x = +2 is also a solution of the first equation.
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Therefore, we have found that y = -2 and x = +2 is the solution for both equations.
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[This means that the (x, y) coordinate point of (+2, -2) is the point where the graphs of the
two original equations cross each other.]
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Hope this helps you to understand the problem and provides you with an understanding of
the process you can follow to solve the set of equations you were originally given.
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