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Solve \(2x + 3y = 11\) and \( 2x – 4y = – 24\)
The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Then she buys 3 bats and 5 balls for Rs.1750. The cost of each bat and each ball is
Let the cost of a bat is x and cost of ball is y
From 1
If a pair of a linear equation is consistent, then the lines are?
The two lines will definitely have a solution.
If the lines \( 3x + 2ky – 2 = 0\) and \( 2x + 5y + 1 = 0\) are parallel, then the value of k is?
The solution of \( x – y = 2 \) and \( x + y = 4\) is?
If x=a, y=b is the solution of the equation \( x + y = 5\) and\( 2x – 3y = 4\), the value of a and b are?
Half the perimeter of a rectangular lawn whose length is 4m more than its width is 36m. The dimensions of the lawn are?
Let the width is x
Length=
Length=
The value of x and y for \( 3x – y = 3, \ 9x – 3y = 9\) is?
Y has infinite values
, so x has infinite values.
The solution of \(x + y = 14\) and \( x – y = 4\) is?
Five years ago, Neera was thrice as old as Sonia. Ten years later, Neera will be twice as old as Sonia. How old are Neera and Sonia?
Let the percentage of Neera is x and present age of Sonia is y.
Also,
On solving 1 and 2 we get,
Y=20
So, age of Neera is 50 years and Sonia is 20 years.
Rita can row downstream 20km in 2 hours and upstream 4km in 2 hours. The speed of rowing in still water is ?
Speed of stream in still water is X km/hr
Speed of stream is Y km/hr
Downstream km/hr
Upstream km/hr
Adding the equations
Students of a class are made to stand in rows. If one student is extra in a row there would be 2 rows less. If one student is less in a row there would be 3 rows more. The numbers of students are?
Let the number of rows is x and number of students in a row is y.
Total number of students is xy
On solving x is 12 and y is 5
Hence, total numbers of students are 60.
8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. The time taken by one man alone is?
Let x be the time taken by man and y be the time taken by boy
According to the question
Let,
So, x ix 140 days and y is 280 days.
In a two digit number the units digits is thrice the tenโs digit. If 36 is added to the number, the digits interchange their place. The number is?
Let unit place is x
Tenโs place is y
X=3y
Number is
Interchanging number is
According to the question
So, number is 26.
If twice the age of son is added to age of father, the son is 56. But if twice the age of father is added to the age of son the sum is 82. The age of father is?
Let fatherโs age will be x years
Let sonโs age will b be y years
According to the question
Equating 1 and 2 together we get,
So, y is equal to 10.
What is a system of simultaneous equations called if its graph has intersecting lines?
When lines intersect the point of intersection is the only point of solution
For what value of k, do the equations \( 3(k – 1)x + 4y = 24\) and \( 15x + 20y = 8(k + 13)\) have infinite solutions.
What is the nature of the graph of a dependent system?
If a graph is of a dependent system, graph will represent the same line.
What is the number of solutions of the pair of linear equations \(\begin{array}{l}4p – 6q + 18 = 0\\2p – 3q + q = 0\end{array}\)
If (P,P) is the solution of equations \(ax + by + (t – s) = 0\) and \( bx + ay + (s – r) = 0\) which of the following must be true?
Put (P,P) in both the equations we get
bP+aP=st
bP+aP=rs
=st=rs
=2s=r+t
If the pair of linear equations \(5x + ky – 3 = 0\) and \( 8x + \dfrac{2}{5}y + k = 0\) has a unique solution, which of the following is true?
What number must be subtracted from each of the numbers 10,11,17,19 to make them proportionate?
Let x be the number
The value of k for which the system of equations \( kx – y = 2, 6x – 2y = 3\) has a unique solution is?
A1=k, b1=1, c1=2
A2=6, b2=2, c2=3
The value of k for which the system of equations \(x + 2y – 3 = 0\) and \( 5x + ky + 1 = 0\) has no solution is?
If the system of equations \(2x + 3y = 7\)\( (a + b)x + (2a – b)y = 21\) has infinitely many solutions, then?
Solving both the equations we get,
A=5, b=1
Raj has some cows and parrots in his shed. The total number of legs is 130 and the total number of heads is 40. The number of cows in shed is?
Let the number of cows be x
Let the number of parrots be y
On solving
The sum of the successors of two numbers is 40 and difference of their predecessors is 8. The numbers are?
Let the two numbers be x and y
Adding equation 1 and 2
Substituting x in equation 2
In a dfraction if numerator is increased by 20 and denominator is decreased by 4, then the dfraction becomes 2. Instead, if numerator is decreased by i4 and denominator is increased by 20, then the dfraction becomes \(\dfrac{2}{5}\). Find the dfraction.
Let the dfraction be
And
On solving both the equations
dfraction
Solve for x and y \(\begin{array}{l}\dfrac{{50}}{{x – y}} + \dfrac{{66}}{{x + y}} = 30\\\dfrac{{60}}{{x – y}} + \dfrac{{77}}{{x + y}} = 33\end{array}\)
Let
On solving equation 3 and 4 we get,
The value of k for which the equations \(x + ky + 30 = 0\) and \(5x + 30y – 150 = 0\) represents parallel lines is?