SOLVING LINEAR EQUATIONS IN TWO VARIABLES GRAPHICALLY WORKSHEET

(1) Form the pair of linear equations in the following problems, and find their solutions graphically.

(i)  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 and girls who took part in the quiz.         Solution

(ii)  5 pencils and 7 pens together cost $50, whereas 7 pencils and 5 pens together cost $46. Find the cost of one pencil and that of one pen.       Solution

(2) On comparing the ratios a₁/a₂, b₁/b₂, c₁/c₂, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.

(i)  5 x – 4 y + 8  =  0 and 7 x + 6 y – 9  =  0

(ii)  9 x + 3 y + 12  =  0 and 18 x + 6 y + 24  =  0

(iii)  6 x - 3 y + 10  =  0 and 2 x - y + 9  =  0

Solution

(3) On comparing the ratios a₁/a₂, b₁/b₂, c₁/c₂,find out whether the following pair of linear equations are consistent or inconsistent.

(i) 3 x + 2 y = 5 and 2 x - 3 y = 7.

(ii) 2 x - 3 y = 8 and 4 x - 6 y = 9

(iii)  (3/2) x + (5/3) y = 7 and 9 x - 10 y = 14

(iii)  (3/2) x + (5/3) y = 7 and 9 x - 10 y = 14

Solution

(4)  Which of the following pairs of linear equations are consistent/inconsistent? if consistent, obtain the solution graphically 

(i)  x + y  =  5  and 2 x + 2 y  =  10

(ii) x - y  =  8 and 3 x - 3 y  =  16

(iii)  2 x + y - 6  =  0 and 4 x - 2 y - 4   =  0

(iv)  2 x - 2 y - 2   =  0 and 4 x - 4 y  - 5  =  0

Solution

(5)  Half the perimeter of a rectangular garden, whose length is 4 m more its width is 36 m. Find the dimensions of the garden.      Solution

(6)  Given the linear equation 2 x + 3 y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

Solution

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