CBSE Class 9 Mental Maths Linear Equation In Two Variables Worksheet

Question. What is an equation?
Answer : An equation is a statement of equality involving one or more unknown quant ities called variable

Question. What is a linear equation in one variable?
Answer : An equation is called a linear equa tion in one variable, if only a single variable with degree one occurs in the equation.

Question. How many solutions does a linear equation in one variable has?
Answer : Only one solution

Question. What is a linear equation in two variables?
Answer : A linear equation in the form of ax + by + c = 0 wher a, b, c are real num bers, a ≠ 0,b ≠ 0 , and x and y are two variables.

Question. How many solutions does a linear equation in two variables have?
Answer : Infinite solutions

Question. What is the value of y in terms of x.  ax+by+c = 0, (a ≠ 0,b ≠ 0)
Answer : y = –c – ax / b

Question. What is the y-form of the equation x−2y = 4 .
Answer : y = x – 4 / 2

Question. What is the x-form of the equation 2x+5y =9.
Answer : y = 9 – 5y / 2

Question. What is the x-form of the equation πx+ y = 9 .
Answer : y = 9 – y / π

Question. Compare the linear equation 3x 8√2y with ax+by+C = 0 and indicate the values of a,b and c.
Answer : a =3,b =− √2,c =−8

Question. Compare 2x =−6y with ax+by+C = 0 , and indicate the values of a,b and c.
Answer : a = 2, b = 6, c = 0

Question. Express x - y/5 - 10 = 0 in the form of ax+by+C = 0 , and indicate the values of a, b and c.
Answer : 5x - y -50 =0, a = 5, b = -1, c =-50

Question. Express x=-9 as a linear equation in two variables.
Answer : x - 0y + 9 = 0

Question. . Express 3y = 7 as a linear equation in two variables.
Answer : 0x+3y - 7 = 0

Question. Express 5y =2 as a linear equation in two variables.
Answer : 0x + 5y -2 = 0

Question. Find whether x = 2 , y = 1 is a solution of a linear equation 5x + 3y = 14.
Answer : No

Question. erify whether x = 12 is a solution of the eqution 0.5x + x/3 = 0.25 + 9.
Answer : No

Question. Examine if x = 0 is a solution of the equation (x - 2) + (x + 3) = x + 8.
Answer : No

Question. Verify if x = 2 is a solution of the equation 3x - 1/4 + 3/4 = 2
Answer : Yes

Question. Examine if 3 is a solution of x - 7 = 3x + 8.
Answer : No

Question. Find the coordinates of the points where the equation 3x + y = 6 intersects both the axis.
Answer : (2, 0) (0, 6)

Question. Find the coordinates of the points where the equation y - 3x = 9 intersects both the axis.
Answer : on x-axis (-3, 0) , on y -axis (0, 9)

Question. Does the point (4,1) lies on the equation 2x + 5y = 13?
Answer : Yes

Question. Find the coordinates of the points where the equation 2x - 3y = 6 intersects x-axis and y-axis.
Answer : x-axis (3, 0) , y-axis - (0, -2)

Question. Find any two solutions for the following linear equations in two variables:
(i) 2x + 5y = 13 (ii) x + y + 4 = 0 (iii) (x - 4) - y + 4 = 0
Find the value of ‘p’ so that the following equations may have x= 1, y = 1 as a solution:
Answer : (i) (4, 1) (1/2 ,12/5
(ii) ( -2, -2) (1, -5)
(iii) (1,1) (2,2)

Question. 3x + py = 6 (27) px - 2y = 10 (28) 5x + 2py = 3a
Represent the given statements as a linear equations in two variables.
Answer : p = 3
p = 12
5p = 3a - 5 / 2

Question. A number is 2/3 of the other number.
Answer : x = 2/3 y

Question. The sum of the ages of a brother and a sister is 50 years.
Answer : x + y = 50

Question. Rupali is 7 times as old as Jayana.
Answer : x = 7y

Question. Two times of a number when added to another number gives 15.
Answer : 2x + y = 15

Question. To which axis the graph of the equation 3x - 2 = 0 is parallel.
Answer : y-axis

Question. o which axis the graph of the equation y = -5 is a line parallel.
Answer : x-axis

Question. At which point the graph of the equation x = -3 intersects x-axis?.
Answer : (-3, 0)

Question. At which point the graph of the equation x + y = 0 intersect x-axis and y-axis?
Answer : 0, 0)

Question.  Which axis does y = 0 represents?
Answer : x- axis

Question. In the graph y = 2 what will be the ordinate for any value of abscissa.
Answer : = 2

Question. In the graph x = -1 what will be the ordinate for any value of abscissa.
Answer : y-axis

Question. To which axis the graph of x = -1 will be parallel to?
Answer : y-axis

Question. How many solutions a linear equation in two variables have?
Answer : Infinite solution

Question. The auto fare in Delhi is as follows: For the first kilometer, the fare of Rs. 10 and for each subsequent distance it is Rs. 5 per km. If the distance covered is x km and the total fare is Rs. y. Represnt this information as a Linear Equation.
Answer :

Question. A pen costs Rs. 10 and a pencil costs Rs. 2. Form an equation that represents the total money spent on buying different combinations of pen and pencils, if the total money spent is Rs. 110.
Answer : 10x + 2y = 110 , where x = no. of pens bought y = no. of pencils boughts.

Question. Verify that which among the following is not a solution of equation 2x - y = 4
Answer : (i) x = 0, y = -4 (ii) x= 3, y = 2 (iii) x = 1, y = 1 (iv) y=0, x = 2
III is not the solution.eeeeeeeeeeeeee

Question. Represent 3x + 5y -11 =0 as y in the form of x. Find the point where the equation intersects y-axis.
Answer : y = 5(x -1) + 10 ⇒ y = 5x + 5