Math, asked by Anonymous, 5 months ago

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the co-ordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.

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Answers

Answered by Anonymous
11

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Answered by MysticalStar07
27

Given that:-

</u><u>\</u><u>sf</u><u> </u><u>x - y + 1 = 0

</u><u>\</u><u>sf</u><u> </u><u>3x  + 2y - 12 = 0

Solving the equation (1)...

\sf x - y + 1 = 0

\sf y = x + 1

Let x = 0,

\sf y = 0 + 1

\sf y = 1

So,

  • x = 0, y = 1 is a solution

  • i.e, (0,1) is the solution.

Let x = 1,

\sf y = 1 + 1

\sf y = 2

So,

  • x = 1, y = 2 is the solution

  • i.e, (1,2) is the solution.

Solving the given equation(2)

</u><u>\sf</u><u> </u><u>3x + 2y  - 12 = 0

</u><u>\sf</u><u> </u><u>2y = 12 - 3x

</u><u>\sf</u><u> </u><u>y =  \</u><u>d</u><u>frac{12 - 3x}{2}

Let x = 0,

</u><u>\sf</u><u> </u><u>y =  \</u><u>d</u><u>frac{12 - 3(0)}{2}

</u><u>\sf</u><u> </u><u>y =  \</u><u>d</u><u>frac{12 - 0}{2}

</u><u>\sf</u><u> </u><u>y =  \cancel \</u><u>d</u><u>frac {12 - 6}{2}

</u><u>\sf</u><u> </u><u>y = 6

So,

  • x = 0, y = 6 is the solution

  • i.e, (0,6) is the solution.

Let x = 2

</u><u>\sf</u><u> </u><u>y =  \</u><u>d</u><u>frac{12 - 3(2)}{2}

</u><u>\sf</u><u> </u><u>y =  \</u><u>d</u><u>frac{12 - 6}{2}

</u><u>\sf</u><u> </u><u>y = \cancel  \</u><u>d</u><u>frac{6}{2}

</u><u>\sf</u><u> </u><u>y = 3

So,

  • x = 2, y = 3 is the solution.

  • i.e, (2,3) is the solution.

Now:-

  • We have to plot both equations on the graph!!

  • Check the graph in the given attachment!!

Therefore,

  • The triangle formed by the lines and x-axis is △ABC.

Where as,

  • A is (2, 3)

  • B is (-1, 0)

  • C is (4, 0)

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