# 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 \((2, \,3)\)