Linear Equations
Practice Linear Equations MCQs from Algebra — Mathematics.
The difference of two numbers is 10 and their ratio is 3:2. Find the smaller number.
For what value of k will the system 2x + 3y = 7 and 4x + ky = 14 have infinitely many solutions?
The sum of a number and its reciprocal is 2. (This results in a linear form if simplified). Find the number.
If 2x + y = 7 and x + 2y = 8, find the value of x - y.
A taxi charge consists of a fixed fee plus a charge per km. If for 10 km the charge is Rs 150 and for 15 km it is Rs 200, find the fixed fee.
Find the value of k for which the system of equations has no solution.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Find the speed of the boat in still water.
Five years ago, a father's age was 7 times his son's age. Five years hence, the father's age will be 3 times his son's age. Find the father's present age.
Solve for x and y: ax + by = a-b and bx - ay = a+b.
A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How long would A take to do the work alone?
Find the values of x and y using the method of cross-multiplication.
The sum of digits of a two-digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number.
For what value of k does the system have a unique solution?
A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. Student A takes food for 20 days and pays Rs 1000. Student B takes food for 26 days and pays Rs 1180. Find the fixed charge.
Solve for x: (x-a)/(b+c) + (x-b)/(c+a) + (x-c)/(a+b) = 3.