Question

# For which of the values of a and b will the following pair of linear equations has infinitely many solutions x + 2y = 1; (a - b)x + (a + b)y = a + b - 2

a) a = - 3 , b = 1

b) a = 3 , b = 1

c) a = 2 , b = 2

d) None of the above

Hint:

### 1. When Both sides of an equation are equal, the said equation is said to have infinitely many solutions.

i.e. When LHS = RHS, the given equation has infinitely many solutions.

2. For Equations with Infinitely Many solutions:-

(a1/a2) = (b1/b2) = (c1/c2)

## The correct answer is: The given equation i.e. 4x - 3 = 2x + 13 can be classified as an equation with only one solution.

### Step-by-step solution:-

x = 2y

∴ x - 2y = 0 .................. (Taking variables and constants on each side of the equation) ............................... (Equation i)

y = 2x

∴ y - 2x = 0 .................. (Taking variables and constants on each side of the equation)

i.e. 2x - y = 0 ..................................................................................... (Equation ii)

Comparing Equations i & ii with the standard form of a linear equation in 2 variables, i.e. ax + by = c, we get-

a1 = 1; b1 = -2; c1 = 0 and

a2 = 2; b2 = -1; c2 = 0

Now, we calculate a1/a2; b1/b2 and c1/c2 to check the corelation between the 3:-

a1/a2 = 1/2 ............................................................................................................................................................ (Equation iii)

b1/b2 = -2/-1 = 2 ....................................................................................................................................................... (Equation iv)

c1/c2 = 0/0 = 0 ......................................................................................................................................................... (Equation v)

From Equations iii, iv & v, We observe that-

a1/a2 ≠ b1/b2 ≠ c1/c2 for the given Equations.

∴ The given Equations have Unique Solution.

Final Answer:-

∴ The given equation i.e. 4x - 3 = 2x + 13 can be classified as an equation with only one solution.

### Related Questions to study

### Describe the pattern in the numbers. Write the next number in the pattern.

3, 1, 1/3, 1/9, …

### Describe the pattern in the numbers. Write the next number in the pattern.

3, 1, 1/3, 1/9, …

### In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find

b) How many answers did each school get correct in the final round?

### In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find

b) How many answers did each school get correct in the final round?

### Classify the linear equations x = 2y and, y = 2x as having one solution, no solution or infinitely many solutions.

### Classify the linear equations x = 2y and, y = 2x as having one solution, no solution or infinitely many solutions.

### In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find

a) Frame the equation which models the scoring in the final round and the outcome of the contest?

### In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find

a) Frame the equation which models the scoring in the final round and the outcome of the contest?

### Use the Law of Detachment to make a valid conclusion in the true situation. If two lines are perpendicular, they form a right angle.

### Use the Law of Detachment to make a valid conclusion in the true situation. If two lines are perpendicular, they form a right angle.

### Classify the linear equations x - 3y = 3 , 3x - 9y = 2 as having one solution , no solution or infinitely many solutions .

### Classify the linear equations x - 3y = 3 , 3x - 9y = 2 as having one solution , no solution or infinitely many solutions .

### Describe the pattern in the numbers. Write the next number in the pattern.

1, 3/4, 1/2, 1/4, …

### Describe the pattern in the numbers. Write the next number in the pattern.

1, 3/4, 1/2, 1/4, …

### Classify the equation 2x + 1 - 4 = -2x - 3 as having one solution , no solution or infinitely many solutions .

### Classify the equation 2x + 1 - 4 = -2x - 3 as having one solution , no solution or infinitely many solutions .

### The Price of Stock A at 9 A.M was 12.73 .Since then the price has been increasing at the rate of Rs 0.06 per hour. At noon , the price of stock B was Rs 13.48 .It begins to decrease at the rate of Rs 0.14 per hour. If the stocks continue to increase and decrease at the same rates, in how many hours will the prices of the stocks be the same?

The equation is defined as a mathematical statement with at least two terms containing variables or numbers that are equal.**Let's take an example:**

Assume the hours are "h" when attempting to equalize,

As per the given question, we can write the equation as:

12.73 + 0.06h = 13.48 - 0.14h

Rearrange the terms of h in the above equation,

0.06h + 0.14h = 13.48- 12.73

In the above equation, combine the corresponding terms,

0.2h = 0.75

Divide both sides by 0.2

h = 0.75/0.2

h = 3.75

Thus, the stock prices will be the same in 3.75 hours.

### The Price of Stock A at 9 A.M was 12.73 .Since then the price has been increasing at the rate of Rs 0.06 per hour. At noon , the price of stock B was Rs 13.48 .It begins to decrease at the rate of Rs 0.14 per hour. If the stocks continue to increase and decrease at the same rates, in how many hours will the prices of the stocks be the same?

The equation is defined as a mathematical statement with at least two terms containing variables or numbers that are equal.**Let's take an example:**

Assume the hours are "h" when attempting to equalize,

As per the given question, we can write the equation as:

12.73 + 0.06h = 13.48 - 0.14h

Rearrange the terms of h in the above equation,

0.06h + 0.14h = 13.48- 12.73

In the above equation, combine the corresponding terms,

0.2h = 0.75

Divide both sides by 0.2

h = 0.75/0.2

h = 3.75

Thus, the stock prices will be the same in 3.75 hours.