Question 70479:
The solution of the system 4x+5y =2 and 6x-2y=b is (3,a). Find the values of a and b.
Helpp Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Start with
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The fact that the point (3,a) satisfies the system of equations (that means it satisfies both equations), tells you that when x = 3 and y = a, the equation
is satisfied. So plug in 3 for x and a for y. When you do, the equation becomes:
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This simplifies to:
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Subtract 12 from each side of this equation to get:
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Finally, divide both sides by 5 to get:
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So now you know that a = -2 and that is one of the things you had to find. You can substitute
this into the point (3,a) which is known to work in both equations because it is the solution
to the system of equations. By substituting -2 for a you know that the point (3, -2) satisfies
both equations.
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The second equation of the system of equations is:
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Since you know this equation is satisfied by x = 3 , y = -2 you substitute these values into
the equation and both sides should be equal. By substitution the equation becomes:
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Multiplying out the terms on the left side results in:
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and adding the two terms on the left side tells you that b = 22. That is the second
quantity that you were supposed to find.
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Hope this helps you to see your way through this word problem OK.
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