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Goryan [66]
3 years ago
6

Solve following x-y=2 5x+3y=18

Mathematics
2 answers:
Mazyrski [523]3 years ago
6 0
x-y=2 \\ -x\ \ -x \\ -y=-x+2 \\ y=x-2 \\ \\ 5x+3(x-2)=18 \\ 5x+3x-6=18 \\ 8x-6=18 \\ +6\ \ \ \ +6 \\ 8x=24 \\ /8\ \ \ /8 \\ x=3
kvasek [131]3 years ago
5 0
X-y = 2
5x+3y =18 

let do some plug and play 

x-y = 2 
x = 2+y
now we got an answer for x lets plug that in the other equation

5(2+y) + 3y = 18
10+5y + 3y = 18
10 + 8y = 18
8y = 8
y = 1 

now lets find x 
x = 2 +y 

x = 2+ 1 
x = 3. 



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I can’t figure out how to use the zeros in the polynomial. Please explain
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Answer:

a) P (x) = (x + 3) (x-1) (x-4)

b) P (x) = (2x + 5) (5x - 4) (x-6)

c) P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2

Step-by-step explanation:

<u>For the question a *</u> you need to find a polynomial of degree 3 with zeros in -3, 1 and 4.

This means that the polynomial P(x) must be zero when x = -3, x = 1 and x = 4.

Then write the polynomial in factored form.

P (x) = (x + 3) (x-1) (x-4)

Note that this polynomial has degree 3 and is zero at x = -3, x = 1 and x = 4.

<u>For question b, do the same procedure</u>.

Degree: 3

Zeros: -5/2, 4/5, 6.

The factors are

x = -\frac{5}{2}\\\\x +\frac{5}{2} = 0\\\\(2x +5) = 0

---------------------------------------

x =\frac{4}{5}\\\\x-\frac{4}{5} = 0\\\\(5x-4) = 0

--------------------------------------

x = 6\\\\(x-6) = 0

--------------------------------------

P (x) = (2x + 5) (5x - 4) (x-6)

<u>Finally for the question c we have</u>

Degree: 5

Zeros: -3, 1, 4, -1

Multiplicity 2 in -1

x = -3\\\\(x-3) = 0

--------------------------------------

x = 1\\\\(x-1) = 0

--------------------------------------

x = 4\\\\(x-4) = 0

----------------------------------------

x = -1\\\\(x + 1) = 0

-----------------------------------------

P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2

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