Linear equation questions are commonly asked in competitive exams, such as:
1. Algebraic manipulation: Solve for x in equations like 2x + 5 = 11 or x - 3 = 7.
2. Graphical representation: Identify the slope and y-intercept from a linear equation in slope-intercept form (y = mx + b).
3. Word problems: Translate real-world scenarios into linear equations, such as "Tom has $15 to spend on lunch, and he wants to buy a sandwich for $8 and a drink for $x. How much can he spend on the drink?"
4. Systems of equations: Solve simultaneous linear equations, like 2x + 3y = 7 and x - 2y = -3.
5. Inequalities: Solve linear inequalities, such as 2x - 5 > 3 or x + 2 ≤ 9.
Some examples of linear equation questions in competitive exams:
- If x + 2 = 9, what is the value of x?
- Find the slope of the line passing through (2,3) and (4,5).
- A bakery sells x loaves of bread at $2 each and y pastries at $5 each. If the total revenue is $100, write an equation to represent the situation.
- Solve the system of equations: x + y = 4 and 2x - 2y = -2.
- If 3x - 2 > 5, what is the range of values for x?
Remember to practice solving various types of linear equation questions to become proficient and confident in your ability to tackle them in competitive exams.
