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miskamm [114]
3 years ago
6

Two solutions of the equation Ax+By = 1 are (2, -1) and (-3,-2). Find A and B.

Mathematics
1 answer:
kati45 [8]3 years ago
4 0

Answer:

Substitute in the values of both given coordinates & form 2 equations:

\left \{ {{A(2)+B(-1)=1} \atop {A(-3)+B(-2)=1}} \right. \\\\=\left \{ {{2A-B=1} \atop {-3A-2B=1}} \right.

Find the value of B from the equation 2A - B = 1:

2A-B=1\\-B=1-2A\\B=2A-1

Substitute in the B-value to the other equation:

-3A-2B=1\\-3A-2(2A-1)=1\\-3A-4A+2=1\\-7A=1-2\\-7A=-1\\A=\frac{-1}{-7} =\frac{1}{7}

Find the B-value using the equation from before:

B=2A-1=2(\frac{1}{7})-1=\frac{2}{7} -\frac{7}{7} =-\frac{5}{7}  

Therefore the equation Ax + By = 1 would equal:

\frac{1}{7} x-\frac{5}{7} y=1

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Step-by-step explanation:

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A = W*L

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Then the area of the rectangle is:

A = (2*x + 9)*(3*x + 1) cm^2

A = (6*x^2 + 2*x + 27*x + 9) cm^2

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now we remove two squares with sides of x cm

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Then the area of the figure will be:

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Now we know that the area of this shape is 83 cm^2, then we need to solve:

83 cm^2 = (4*x^2 + 29*x + 9) cm^2

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Then we need to solve:

0 = 4*x^2 + 29*x - 74

Here we can use Bhaskara's equation, the solutions of this equation are given by:

x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)}  }{2*4} = \frac{-29 \pm 45}{8}

Then the two solutions are:

x = (-29 - 45)/8 = -9.25  (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).

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x = (-29 + 45)/8 = 2

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Then the length and width of the rectangle are:

Length = (2*2 + 9)cm = 13 cm

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