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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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.
Answer fast
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Verified answer
Given that:-
[tex]\sf x - y + 1 = 0[/tex]
[tex]\sf 3x + 2y - 12 = 0[/tex]
Solving the equation (1)...
[tex]\sf x - y + 1 = 0[/tex]
[tex]\sf y = x + 1[/tex]
Let x = 0,
[tex]\sf y = 0 + 1[/tex]
[tex]\sf y = 1[/tex]
So,
Let x = 1,
[tex]\sf y = 1 + 1[/tex]
[tex]\sf y = 2[/tex]
So,
Solving the given equation(2)
[tex]\sf 3x + 2y - 12 = 0[/tex]
[tex]\sf 2y = 12 - 3x[/tex]
[tex]\sf y = \dfrac{12 - 3x}{2} [/tex]
Let x = 0,
[tex]\sf y = \dfrac{12 - 3(0)}{2} [/tex]
[tex]\sf y = \dfrac{12 - 0}{2} [/tex]
[tex]\sf y = \cancel \dfrac {12 - 6}{2} [/tex]
[tex]\sf y = 6[/tex]
So,
Let x = 2
[tex]\sf y = \dfrac{12 - 3(2)}{2} [/tex]
[tex]\sf y = \dfrac{12 - 6}{2} [/tex]
[tex]\sf y = \cancel \dfrac{6}{2} [/tex]
[tex]\sf y = 3[/tex]
So,
Now:-
Therefore,
Where as,