Ex.3.2 Q7 Pair of Linear Equations in Two Variables Solution - NCERT Maths Class 10

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Question

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

 Video Solution
Pair Of Linear Equations In Two Variables
Ex 3.2 | Question 7

Text Solution

What is Known?

Linear equation

\[\begin{align}x - y + 1 &= 0\\3x + 2y-12 &= 0\end{align}\]

What is Unknown?

Coordinates of the vertices of the triangle formed by intersecting lines and the \(x\)-axis

Reasoning:

From graph of two linear equations and \(x\)-axis, triangle can be shaded, and vertices can be located.

Steps:

\[\begin{align}x - y + 1 &= 0\\y &= x + 1\end{align}\]

\(x\) \(0\) \(1\)
\(y = x + 1\) \(1\) \(2\)

\[\begin{align}3x + 2y-12 &= 0\\2y &= 12 - 3x\\y &= \frac{{12 - 3x}}{2}\end{align}\]

\(x\) \(0\) \(2\)
\(y = \frac{{12 - 3x}}{2}\) \(6\) \(3\)

From graph, Vertices are \((-1, \,0),\; (4,\, 0),\) and \((2, \,3)\)