LINEAR EQUATIONS IN TWO VARIABLES
1: For what value of c, the linear equation 2x+cy = 8 has equal values of x and y for its solution?
2: If the point (3,4)lies on the graph of 3y = ax + 7,find a.
3: The coordinates of points in the table represent some of the solutions of the equation x – y+2=0.State whether the
given statement is true or false. Justify.
x 0 1 2 3
y 2 3 4 -5
4: Draw the graph of equation 2x + 3y + 6 = 0. Find the points at which it cuts the x-axis and y - axis.
5: Determine the point on the graph of the equation 2x+5y=19 ,whose ordinate is 11
2
times its abscissa.
6: A person bought x kg of apples@ Rs.13/kg and y kg of potatoes
@Rs. 11/kg. He paid ₨133. Write the equation for this. Draw the graph for it. What will be the quantity of apples if 2 kg
of potatoes were purchased, when the paid amount remains the same.
7: The graph of the equation x=-3 is parallel to ----------------.
8: Y=0 is the equation of -----------------.
9: Draw the graphs of equation 2x+y=6,2x – y+2=0. Find the point of intersection, and the points where the graphs of
both the equations cut X-axis and Y-axis respectively.
10: Express the equation 15x+2y=1750 in the form of ax+ by + c = 0, find a, b, c.
11: The total runs scored by two batsmen in a cricket match are 160. Write a linear equation in two variables x and y.
Also, represent it on the graph.
12: Give the geometrical representation of x – 5=2x+4 in
One variable
Two variables
13: Express 2
3
=
6
+5 in the form ax+by+c=0.
14: Find the area of the triangle formed by the line x+3y =12 and the coordinate axes.
15: The taxi fare in a city is such that ₨. 50 is the fixed amount and ₨.16 per km. is charged. Taking the distance
covered as x km and total fare as ₨. y, write a linear equation in x and y. Find the total fare for 20 km.
Answers
Given : the linear equation 2x+cy = 8 has equal values of x and y for its solution
To find : Value of c
Solution:
2x+cy = 8
equal values of x and y for its solution
=> x = y
=> 2x + cx = 8
=> x (2 + c) = 8
=> x = 8 /(2 + c)
many possible solutions
Few examples :
c = 2 => x = 2 , y = 2
c = 6 => x = 1 , y = 1
c = 2 if c = x = y
point (3,4)lies on the graph of 3y = ax + 7
=> 3(4) = a(3) + 7
=> 12 = 3a + 7
=> 3a = 5
=> a = 5/3
Please post question one by one
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Answer:
1: For what value of c, the linear equation 2x+cy = 8 has equal values of x and y for its solution?
2: If the point (3,4)lies on the graph of 3y = ax + 7,find a.
3: The coordinates of points in the table represent some of the solutions of the equation x – y+2=0.State whether the
given statement is true or false. Justify.
x 0 1 2 3
y 2 3 4 -5
4: Draw the graph of equation 2x + 3y + 6 = 0. Find the points at which it cuts the x-axis and y - axis.
5: Determine the point on the graph of the equation 2x+5y=19 ,whose ordinate is 11
2
times its abscissa.
6: A person bought x kg of apples@ Rs.13/kg and y kg of potatoes
@Rs. 11/kg. He paid ₨133. Write the equation for this. Draw the graph for it. What will be the quantity of apples if 2 kg
of potatoes were purchased, when the paid amount remains the same.
7: The graph of the equation x=-3 is parallel to ----------------.
8: Y=0 is the equation of -----------------.
9: Draw the graphs of equation 2x+y=6,2x – y+2=0. Find the point of intersection, and the points where the graphs of
both the equations cut X-axis and Y-axis respectively.
10: Express the equation 15x+2y=1750 in the form of ax+ by + c = 0, find a, b, c.
11: The total runs scored by two batsmen in a cricket match are 160. Write a linear equation in two variables x and y.
Also, represent it on the graph.
12: Give the geometrical representation of x – 5=2x+4 in
One variable
Two variables
13: Express 2
3
=
6
+5 in the form ax+by+c=0.
14: Find the area of the triangle formed by the line x+3y =12 and the coordinate axes.
15: The taxi fare in a city is such that ₨. 50 is the fixed amount and ₨.16 per km. is charged. Taking the distance
covered as x km and total fare as ₨. y, write a linear equation in x and y. Find the total fare for 20 km.
Step-by-step explanation: