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4 years ago

Solve the system of equations.

2 answers:

7 0

2x - 5y = 3
x - 3y = 1...multiply by -2
---------------
2x - 5y = 3
-2x + 6y = -2 (result of multiplying by -2)
--------------add
y = 1

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

solution is (4,1)

BartSMP [9]4 years ago

6 0

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

$2x-5y = 3\\\\ x -3y = 1$

Now, we will use "Substitution Method" to find the values of x and y:

$x=1+3y\ -(3)$

Put the value of x in first equation i.e.

$2x-5y = 3$

$2(1+3y)-5y=3\\\\2+6y-5y=3\\\\2+y=3\\\\y=3-2\\\\y=1$

Now, we use the value of y in equation (3),

$x=1+3y\\\\x=1+3\times1\\\\x=1+3\\\\x=4$

Hence, values of (x,y) is (4,1).

Therefore, First Option is correct.

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4 years ago

Write the fifteenth term of the binomial expansion of (a^2+b)^20

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Answer:

The fifteenth term of the binomial expansion of $(a+b)^{20}$ is $38760\cdot a^{6}\cdot b^{14}$ .

Step-by-step explanation:

Let be a binomial of the form $(a+b)^{n}$ , where $a, b\in \mathbb{R}$ and $n\,\in\mathbb{N}^{+}$ . The expansion of this polynomial is defined below:

$(a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})$ (1)

Where:

$n$ - Number of terms of the expanded polynomial.

$k$ - Index associated to $k$ -th term of the expanded polynomial.

For all $n$ -th binomial, we a sum of $n+1$ terms. If the given binomial has a term of $20$ , then we have 21 terms and the fifteenth term of the polynomial corresponds to the $14$ -th term. Then, the fifteenth term of the binomial is: