Chapter 3 – Pair of Linear Equations in Two Variables

Find the dimensions of a garden, whose length is 4 m more than its width and half the perimeter is 36 m.

The sides of a triangle are AB, BC and AC whose equations are respectively y-2 = 0; y = 3x – 7 and 2y + x = 0, The coordinates of points A and B are :

Given is the system of Inconsistent equations, 2x + 7y = 11 and 5x + ky – 25 = 0, find k.

10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys who took part in the quiz.

5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens cost Rs. 46. Find the cost of 2 pencils and 3 pens.

A linear equation in two variables has:

A pair of linear equations is not consistent if:

In a AABC, ∠A = x°, ∠B = (3a – 2)° and ∠C = y°. Also, ∠C – ∠B = 9°. Find the value of ∠B.

The perimeter of a rectangle is 44 cm. Its length exceeds twice its breadth by 4 cm. Find the area of the rectangle.

For what value of k, will the equations, x + 2y + (11 – k) = 0 and 2x + ky + (10 + k) = 0 represent the coincident lines :

An equation ax + by + c = 0 is a linear equation in 2 variables, where a, b, c are :

Equation of line m is :

The pair of equations y = 9 and y = – 7 has:

The system of equations 3x – 5y = 20 and 6x – 10y = 40 has :

For what value of a, the pair of equations, 3x + 2y – 4= 0 and ax – y – 3 = 0 has a unique solutions :

The sum of a two digit number is 8. The number obtained by reversing the digits exceeds the number by 18. Then the given number is :

In a triangle, the sum of two angles is equal to the third angle. If the difference between two angles is 30°, find the angles.

Question 18.

The line x – y + 1 = 0 meets Y-axis at:

The solutions of the system of equations, x – y + 1 = 0, 3x + 2y -12 = 0 is :

The area of triangle formed by x-y +1 = 0, 3x + 2y -12 = 0 and X-axis is :

The area of triangl e formed by x – y +1 = 0, 3x + 2y -12 = 0 and x = 0 is :

Find the value of (x + y) if 148x + 231y=527 and 231x + 148y = 610.

The line x = 4 :

If x and y satisfy the given two equations, 4x + \(\frac{6}{y}\) = 15, 6x – \(\frac{8}{y}\) = 14; find p is y = px – 2.

Find the value which k cannot take, for the given system to have a unique solutions, x + 2y = 3, ky + 5x + 7 = 0.

Find p and q so that given system has infinite number of solutions, 4x + 6y -14 = 0.(p + q)x + (2 p – q)y – 3 (p + q +1) = 0

Find x and y in the given rectangle :

Equation of line l is,

Equation of line m is :