Solve 5x + 4/y =7 and 4x + x/y =5 simultaneously.
1 answer:
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Answer:
(x, y) ≈ (1.1642, 3.3930) and (3.4358, -0.39297)
Step-by-step explanation:
Solve the first equation for y, then substitute into the second.
5x +4/y = 7
4/y = 7 -5x
4/(7 -5x) = y
Then the second equation becomes ...
4x +x/(4/(7 -5x)) = 5
4x +x(7 -5x)/4 = 5
16x +7x -5x^2 = 20 . . . . . multiply by 4
5x^2 -23x +20 = 0 . . . . . put in standard form
We can use the quadratic formula to solve this.
x = (23±√((-23)² -4(5)(20)))/(2(5)) = (23±√129)/10
x = 2.3 ±√1.29 ≈ {1.1642, 3.4358}
y = 4/(7 -5x) = {3.3930, -0.39297}
Solutions are (x, y) ≈ (1.1642, 3.3930) and (3.4358, -0.39297).
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Part 3) The unit rate is
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see the attached figure
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
where
d ----> number of dollars (dependent variable or output value)
n ---> number of ounces (independent variable or input value)
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<u><em>Verify each case</em></u>
1) we have
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The slope is
therefore
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2) we have
<em>First table</em>
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(4,1) and (16,4)
substitute in the formula of slope
simplify
therefore
The unit rate is
3) we have
This is a proportional relationship between the variables d and n
isolate the variable d
The slope is
therefore
The unit rate is
4) we have
<em>Second table</em>
take two points from the table
(1,4) and (2,8)
substitute in the formula of slope
therefore
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