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3 years ago

Find the solution to the system of equations by substitution. 2x - 2y = - 6 y= 2x

Mathematics

1 answer:

dusya [7]3 years ago

7 0

Answer:

x = -2

y = 2

Step-by-step explanation:

Take the value of x from the first equation: x = 2 − 2 y ( 1 ) , and substitute for x into the second: y = 2 ( 2 − 2 y ) + 6 solve for y ; y = 4 − 4 y + 6 y = 10 5 = 2 Substitute back into ( 1 ) and find x : x = 2 − 4 = − 2

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Answer:

Largest prime factor of the given expression is 379.

Step-by-step explanation:

Given the expression:

$15^6 - 7^6$

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

$15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)$

Let us learn two formula:

$x^3+y^3 = (x+y)(x^2+y^2-xy)$

$x^3-y^3 = (x-y)(x^2+y^2+xy)$

Applying the above formula in the expression written above:

$(15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2$ ...... (1)

Similarly:

$(15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379$ ........ (2)

Multiplying the expressions from (1) and (2) to get the result:

$\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2$

So, largest prime factor of the given expression is 379.

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3 years ago