SOLUTION: y=2x-7 y=-5x+14

Question 476398: y=2x-7
y=-5x+14
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You are given two equations as follows:
.
y = 2x - 7 and
y = -5x + 14
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You can solve this equation by substitution. Look at the top equation. Notice what y equals. It equals 2x - 7.
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You can now go to the bottom equation and substitute 2x - 7 for y. When you do that substitution, the bottom equation becomes:
.
2x - 7 = -5x + 14
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Solve this equation by moving the -7 to the right side. This is done by adding +7 to both sides as follows:
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2x - 7 + 7 = -5x + 14 + 7
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The sevens on the left side cancel because they have opposite signs and on the right side the 7 adds to the 14 to give 21. So the equation becomes:
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2x = -5x + 21
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Now move the -5x from the right side to the left side by adding +5x to both sides as follows:
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2x + 5x = -5x + 5x + 21
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On the right side the -5x and +5x cancel each other out because of the difference in their signs. On the left side the 5x adds to the 2x to give 7x. So the equation becomes:
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7x = 21
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Finally, solve for x by dividing both sides by 7 and you get:
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x = +3
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Now that you know the value of x, you can find the value of y as follows: return to either of the given equations and substitute +3 for x. Then calculate the corresponding value of y. For example, return to the top equation:
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y = 2x - 7
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Substitute +3 for x and this equation becomes:
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y = 2(+3) - 7
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Do the multiplication on the right side and you get:
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y = 6 - 7
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Combine the terms on the right side and you get the value of y as:
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y = -1
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So, the answer is that for the two equations you were given, both equations have the common solution x = 3 and y = -1.
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Just as a check, return to the bottom equation and substitute +3 for x and see if you don't get -1 as the value for y:
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y = -5x + 14
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y = -5(+3) + 14
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y = -15 + 14
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y = -1
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This checks out so the answer of x = 3 and y = -1 is correct.
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Hope this helps you to understand the problem.
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