In this page Cross Multiplication Method Questions 1 we are going to see solution for first problem of the worksheet cross multiplication method.
While solving a pair of linear equations in two unknowns x and y using elimination method,we have to think about how to eliminate any one of the variable in two equations to get value of one unknown and we have to plug it in the second to get the value of other variable. There is another method called cross multiplication which simplifies the procedure.
Solve the following system of equations using cross multiplication method
(i) 3 x + 4 y = 24, 20 x - 11 y = 47
First we have to make the given equations in the form of a₁ x + b₁ y + c₁ = 0,a₂ x + b₂ y + c₂ = 0.
3 x + 4 y - 24 = 0 ----- (1)
20 x - 11 y - 47 = 0 ----- (2)
x/(-188-264) = y/(-480 -(-141)) = 1/(-33-80)
x/(-452) = y/(-480+141)) = 1/(-33-80)
x/(-452) = y/(-339) = 1/(-113)
x/(-452) = 1/(-113) y/(-339) = 1/(-113)
x = (-452)/(-113) y = (-339)/(-113)
x = 4 y = 3
Therefore solution is (4,3).
Now let us apply the answer that we got in the first or second equation to check whether we got correct answer or not.
3 x + 4 y = 24
3(4) + 4(3) = 24
12 + 12 = 24
24 = 24 cross multiplication method question1 cross multiplication method question1
Formulate the following problems as a pair of equations,and hence find their solutions:
(i) One number is greater than thrice the other number by 2. If 4times the smaller number exceeds the greater by 5, find the numbers.
(ii) The ratio of income of two persons is 9:7 and the ratio of their expenditure is 4:3.If each of them manages to save $2000 per month, find their monthly income.
(iii) A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.
(iv) Three chairs and two tables cost $700 and five chairs and three tables cost $1100.What is the total cost of 2 chairs and 3 tables.
(v) In a rectangle,if the length is increased and breadth is reduced each by 2 cm then the area is reduced by 28 cm². If the length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm². Find the area of the rectangle.
(vi) A train traveled a certain distance at a uniform speed. If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time. If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train.