SELF TEST:
1. Form the pair of linear equations in the following problems, and find their solutions graphically.
10 bedsheets and 5 table covers together cost Rs 1550, whereas 7 bedsheets and 4 table covers together cost Rs 1200. Find the cost of one bedsheet and one table cover. ( 3 mk)
2. On comparing the ratios 
find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: ( 2 mk )
( i ) 6 x + 4 y – 30 = 0 : 5 x + 3 y – 20 = 0
3. On comparing the ratios , find out whether the following pair of linear equations are consistent, or inconsistent. ( 2 mk )
( i ) 7 x + 5 y = 20, 6 x − 3 y = 1 5
4. Which of the following pairs of linear equations are consistent / inconsistent? If consistent, obtain the solution graphically( 3 mk )
( i ) 3 x + 2 y = 12, (ii) 2 x + 4 y = 16
5. Half the perimeter of a rectangular garden, whose length is 3 m more than its width, is 30 m. Find the dimensions of the garden. ( 2 mk )
6. Draw the graphs of the equations 3 x – 4 y + 10 = 0 and 2 x + 5 y – 18 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x axis, and shade the triangular region.( 4 mk )
7. Armaan tells his niece, “Nine years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically. ( 4 mk )
8. The cost of 5 kg of sand and 3 kg of cement on a day was found to be Rs 445. After a month, the cost of 4 kg of sand and 4 kg of is cement Rs 550. Represent the situation algebraically and geometrically. .( 4 mk )
9. Solve the following pair of linear equations by the substitution method.
12 x – 3 y = 9 : 6 x – 9 y = 18 .( 2 mk )
10. Solve 4 x + 5 y = 16 and 2 x – 4 y = – 14 and hence find the value of ‘m’ for
which y = m x + 3. (3 mk )
11.Form the pair of linear equations for the following problems and find their solution by substitution method. .( 4 mk )
( a ) The difference between two numbers is 18 and one number is three times the other. Find them.
( b ) The larger of two supplementary angles exceeds the smaller by 32 degrees. Find them.
12. Solve the following pair of linear equations by the elimination method and the substitution method : ( 4 mk )
( a ) x + 3 y = 18 and 2 x – 3 y = 15.
( a – b ) x + ( a + b ) y = 3 a + b – 2