Question 128663
Sure you can grasp this. 
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The fundamental thing you need to understand is that coordinate points are always of the
form (x, y). So the first value inside the parentheses is the value of x and the second value
(after the comma) is the value of y. So the point (?, 20) tells you that you don't know the
value of x, but the value of y is 20. So, you go to the equation:
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{{{2x + (1/5)y = 6}}}
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and you substitute 20 for y and then you solve for x. Substituting 20 for y in the equation 
results in:
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{{{2x + (1/5)*20 = 6}}}
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And one-fifth of 20 is 4 which further reduces the equation to:
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{{{2x + 4 = 6}}}
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Get rid of the 4 on the left side by subtracting 4 from both sides and you have:
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{{{2x = 2}}}
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Finally solve for x by dividing both sides of this equation by 2, the multiplier of x, and
you get:
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{{{x = 2/2 = 1}}}
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So you now know that when y equals 20, x equals -1. So the coordinate point you are looking
for is (1, 20)
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In the second part of this problem you are given the point (9/5, ?}. This tells you
that {{{x = 9/5}}} and you are to solve for y. Go to the equation again and this time substitute
{{{9/5}}} for x and solve for y. The original equation was:
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{{{2x + (1/5)y = 6}}}
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Substitute {{{9/5}}} for x and you have:
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{{{2*(9/5)+(1/5)y = 6}}}
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Multiply the 2 times {{{9/5}}} and you get {{{18/5 }}} making the problem become:
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{{{18/5 +(1/5)y = 6}}}
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Get rid of the {{{18/5}}} on the left side by subtracting {{{18/5}}} from both sides, making
the equation become:
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{{{(1/5)y = 6 -(18/5)}}}
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You can now get rid of the {{{1/5}}} on the left side by multiplying both sides of this equation
(all terms in the equation) by 5 to make the equation become:
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{{{y = 30 - 18}}}
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Now just solve for y by algebraically combining the two terms on the right side to get:
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y = 12
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So the answer to the second problem is that the coordinate point is (9/5, 12)
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Hope this helps to cure your headache.
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