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nirvana33 [79]
3 years ago
12

2x+y=1 9x + 3y = -3 The x-coordinate of the point of intersection is

Mathematics
2 answers:
bija089 [108]3 years ago
5 0

Answer:

Step-by-step explanation:

Hello there!

If we have two equations, two lines and they intersect the key here is to find the value for x, then for y. By doing this we'll find the cartesian point for their common point. The point of intersection.

So Let us set the System of Linear equations. Solving it using the Addition Method.

\left \{{{2x+y=1}\atop {9x+3y=-3}}\right. \\ \left \{{{2x+y=1}*(-3)\atop {9x+3y=-3}}\right. \\\left \{{{-6x-3y=-3}\atop {9x+3y=-3}}\right. \\\\ 3x :3=-6 :3\\ x=-2\\ \\2(-2)+y=1\\ y=5\\

So the point of intersection is (-2,5) and x-coordinate is x=-2

Anvisha [2.4K]3 years ago
4 0
Hello : 
<span>2x+y=1 ....(1)
9x + 3y = -3....(2)
by (1) : y = -2x+1...(*)
by (2) : 3(3x+y) = - 3
3x+y = -1
y = -3x -1 ....(**)
by (*) (**) :
-2x+1 = -3x -1
- 2x +3x = -1 -1 
x =-2  is </span><span>The x-coordinate of the point of intersection</span>
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A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther
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<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\

Therefore, on checking, we observe that,

a_{n}=a_{n-1}+(n-1)^{2}

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0

which is true.

<u>At, </u>

<u>n = 2</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1

Which is also true.

<u>At, </u>

<u>n = 3</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5

Which is true.

<u>At, </u>

<u>n = 4</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

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