Question

Q30) Draw the graph of given equation on same graph paper and find the point of intersection .
3x+y = 7 ; x-2y = 0​

Answer 1

EXPLANATION.

Graph of the equation on same graph paper,

(1) = 3x + y = 7.

(2) = x - 2y = 0.

(1) = 3x + y = 7.

From equation (1) we get,

Put x = 0 in equation, we get.

⇒ 3(0) + y = 7.

⇒ 0 + y = 7.

⇒ y = 7.

Their Co-ordinates = (0,7)

Put y = 0 in equation, we get.

⇒ 3x + 0 = 7.

⇒ 3x = 7.

⇒ x = 7/3 = 2.33.

Their Co-ordinates = (2.33,0).

(2) = x - 2y = 0.

Put x = o in equation, we get.

⇒ 0 - 2y = 0.

⇒ y = 0.

Their Co-ordinates = (0,0).

Put y = 0 in equation, we get.

⇒ x - 2(0) = 0.

⇒ x = 0.

Their Co-ordinates = (0,0).

Red curves indicates the equation = 3x + y = 7.

Blue curves indicates the equation = x - 2y = 0.

Both curves intersects at point (2,1).

Answer 2

$\large\underline{\red{\sf \orange{\bigstar} .}}$Equation Given in a question

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

•—:: (i) = 3x + y = 7.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

•—:: (ii) = x - 2y = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

(i) = 3x + y = 7.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☯ From equation (1) we have;

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☯ Putting x = 0 in equation, we have;

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ 3(0) + y = 7.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ 0 + y = 7.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ y = 7.✔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☯ The Co-ordinates calculated = (0,7) ✔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⚛ Put y = 0 in equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ 3x + 0 = 7.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ 3x = 7.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ x = 7/3 = 2.33.✔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \pink{\bigstar} .}}$The Co-ordinates calculated= (2.33,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

(ii) = x - 2y = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \blue{\bigstar} .}}$Put x = o in equation, we have;

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ 0 - 2y = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ y = 0.✔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \pink{\bigstar} .}}$The Co-ordinates calculated = (0,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \purple{\bigstar} .}}$Put y = 0 in equation, we have;

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦ x - 2(0) = 0

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➦x = 0 ✔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \pink{\bigstar} .}}$The Co-ordinates calculated = (0,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \green{\bigstar} .}}$Both the curves will intersects at point $\pink{\sf{\star\;(2,1)}}$ on graph as shown above .$\large\underline{\red{\sf \green{\bigstar} .}}$

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