Arrangement: Given, the conditions for diagrams are \[x-y\text{ }+\text{ }1\text{ }=\text{ }0\] and ...
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) Intersecting lines (ii) Parallel lines (iii) Coincident lines Arrangements: (I) Given the straight condition \[2x\text{ }+\text{ }3y\text{ }\text{ }8\text{ }=\text{ }0\] . To track down one more...
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Solutions: Let us consider. The width of the nursery is \[x\] and length is \[y\] . Presently, as per the inquiry, we can communicate the given condition as; \[y-x\text{ }=\text{ }4\] also,...
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
Given, \[2x\text{ }+\text{ }y-6\text{ }=\text{ }0\text{ }and\text{ }4x-2y-4\text{ }=\text{ }0\] $\left( a1/a2 \right)\text{ }=\text{ }2/4\text{ }=\text{ }1/2$ ...
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i) x + y = 5, 2x + 2y = 10 (ii) x – y = 8, 3x – 3y = 16 Arrangements: (i) \[x\text{ }+\text{ }y\text{ }=\text{ }5\text{ }and\text{ }2x\text{ }+\text{ }2y\text{ }=\text{ }10\] ...
On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether the following pair of linear equations are consistent, or inconsistent.
(i)(3/2)x+(5/3)y = 7; 9x – 10y = 14 (ii) 5x – 3y = 11 ; – 10x + 6y = –22 (iii)(4/3)x+2y = 8 ; 2x + 3y = 12 (i)Given \[\left( 3/2 \right)x\text{ }+\text{ }\left( 5/3 \right)y\text{ }=\text{ }7\text{...
On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether the following pair of linear equations are consistent, or inconsistent.
(i) 3x + 2y = 5 ; 2x – 3y = 7 (ii) 2x – 3y = 8 ; 4x – 6y = 9 Arrangements: (I) Given : \[3x\text{ }+\text{ }2y\text{ }=\text{ }5\text{ }or\text{ }3x\text{ }+\text{ }2y\text{ }-\text{ }5\text{...
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) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 Arrangements: (I) Given articulations; \[5x\text{ }\text{...
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. (ii) 5 pencils and...