System of equations - practice problems
A system of equations consists of two or more equations with multiple variables that are solved simultaneously to find values satisfying all equations at once. Common types include linear systems, which can be solved using substitution, elimination, or matrix methods. Systems can have one unique solution (consistent and independent), infinitely many solutions (consistent and dependent), or no solution (inconsistent). Graphically, solutions represent intersection points of the equations' graphs. Systems of equations model real-world situations involving multiple constraints, such as supply and demand, mixture problems, and network flows. Advanced topics include systems of non-linear equations and applications in optimization and linear programming.Number of problems found: 2130
- Carnival
Kevin is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $3. Kevin spent $18 altogether at the carnival and the number of games he played is 4 times the number of rides he went on. Write a system of equations that c - Two sons and man
A man's age is three times the sum of the ages of his two sons. After five years, his age will be twice the sum of the ages of his two sons. Find the age of the man. - Father and son
Age of father is 5 times the age of his son. After 10 years, age of father will be 3 times the age of son. Find the present age of both of them . - Daughter and Mom A mother is seven times as old as her daughter. In 7 years time she will be five times as old as her daughter. How old is each of them?
- Mother and daughter 6 A mother is six time as old as her daughter. In 6 years time she will be four times as old as her daughter . How old is each of them?
- Alcohol mixture 3
A mixture contains alcohol and water in the ratio 4:3. If 7 liters of water is added, the ratio of alcohol and water becomes 3:4. Find the quantity of alcohol in the mixture. - The profit 6
A man sells an article at a profit of 20%. If he had bought it at 20% less and sold for $5 less, he would have gained 25%. Find the cost price of the article. - A train 7
A train overtakes two persons. They are walking in the same direction as the train at the rate of 2 km/hr and 4 km/hr. The train passes them completely in 9 and 10 seconds respectively. Find the length of the train. - Two types of ore
A total of 42 tons of two types of ore is to be added into a smelter. The first type contains 6% copper and the other contains 2.5% copper. Find the necessary amounts of each ore to produce 2 tons of copper. - Digits sum
A two digit number is 3 times the sum of its digits. If 45 is added to the number, its digits are interchanged. Find the sum of the digits of the number. - The sum 52 The sum of digits of a two digits number is 10. On interchanging the digit, the number obtained is 54 less than the original number. What is the original number?
- The ratio 21
The ratio between the number of sides of two regular polygon is 1:2 and ratio of sum of their interior angles is 2:3. Find their number of sides. - The ages 3 The ages of A and B are in ratio of 5:4. Three years hence the ratio of their ages will become 11:9. What is the present age of B?
- A rectangle 15
A rectangle is 5 cm longer its width. It areas is 6 cm square. What are the dimensions of the rectangle. - A man 24
A man distributed 25300 EUR among his 3 sons A, B, C in such a way that the amounts of their parts at 10% simple interest in 2 years, 3 years, 4 years will be equal. A's share? - The angle 9
The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 m towards the foot of the tower to a point B, the angle of elevation increases to 60°. Find the height of the tower and the distance of the tower - Susan 5
Susan has a water tank in his back garden that can hold up to 750L in water. At the start of a rainy day (at 0:00) there is 165L in the tank, and after a heavy day’s rain (at 24:00) there is 201 L in the tank. Assuming that the rain fell consistently duri - The sum 51
The sum of two numbers is 100 and difference is 37 . Find the difference between their squares. - 5 yrs 5 yrs ago, the average age of Rasmi and Suravi was 20 yr. Now, the average age of Rasmi, Suravi and Mita is 30 yrs. What will be the age of Mita after 15 years?
- The boat
A boatman goes 2 km against the stream in 40 minutes and returns to the same spot in 30 minutes. What is his rate of rowing in still water?
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