Question

Give the generatic representation of 3x+5=6x-10 with solution

Answer 1

3x - y = 5 this is your answer

Answer 2

Answer:

4

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Syllabus

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Show graphically that the system of equations 3x - y = 5, 6x - 2y = 10 has infinitely many solutions.

SOLUTION

On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x-axis and y-axis, respectively.

Graph of 3x - y = 5

3x - y = 5

⇒y = 3x -5 …(i)

Putting x = 1, we get y = -2

Putting x = 0, we get y = -5

Putting x = 2, we get y = 1

Thus, we have the following table for the equation 3x - y = 5

x 1 0 2

y -2 -5 1

Now, plot the points A(1, -2), B(0, -5) and C(2, 1) on the graph paper.

Join AB and AC to get the graph line BC. Extend it on both ways.

Thus, the line BC is the graph of 3x - y = 5.

Graph of 6x - 2y = 10

6x - 2y = 10

⇒ 2y = (6x – 10)

⇒ y =

6x−102 …(ii)

Putting x = 0, we get y = -5

Putting x = 1, we get y = -2

Putting x = 2, we get y = 1

Thus, we have the following table for the equation 6x - 2y = 10.

x 0 1 2

y -5 -2 1