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tigry1 [53]
3 years ago
15

What are the solutions to the following system of equations? Select the correct answer. y=x^2-4x+8 4x+y=12

Mathematics
2 answers:
Murrr4er [49]3 years ago
8 0
Reduce the second equation to y= -4x + 12, then subtract the two equations. (Quadratic on top), to get y=x^2 -4. Then, plug in an x,y coordinate if you have one.
lorasvet [3.4K]3 years ago
7 0
Y=x^2-4x+8 and 4x+y=12 so y=12-4x, insert y in the quadratic to get
12-4x=x^2-4x+8
12=x^2+8
0=x^2-4=(x-2)(x+2)
So the solutions are x=2 and x=-2.
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Answer:

\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}

Step-by-step explanation:

Given

\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}

Required

Fill in the gaps

Going by the given parameters, we have that

\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}

x^2 - 9x + 8, when factorized is (x-1)(x-8)

Hence; the expression becomes

\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}

Combine Fractions

\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}

Simplify the denominators

4x + 2 = A + B

By direct comparison

A = 4x

B = 2

Hence, the complete expression is

\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}

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