## 1. Which of the following pair of equations has a unique solution?

### Answer:

### Explanation:

The given lines have different slopes and hence they intersect at a unique point.

## 2. The system of equations x + y = 5 and 2x + 2y = 10 has:

### Answer:

### Explanation:

The second equation is just a multiple of the first. Thus, they represent the same line, leading to infinite solutions.

## 3. If the lines represented by the equations ax + by = c and bx – ay = 1 are perpendicular, then:

### Answer:

### Explanation:

The product of the slopes of two perpendicular lines is -1.

## 4. The point of intersection of the lines 2x – y = 3 and x + y = 2 is:

### Answer:

### Explanation:

On solving the two equations, we get x=1 and y=1.

## 5. The lines represented by the equations x – 2y = 3 and 2x – 4y = 6 are:

### Answer:

### Explanation:

Both equations represent the same line.

## 6. The condition for the equations ax + by = c and bx + ay = d to represent coincident lines is:

### Answer:

### Explanation:

For coincident lines, the ratios of coefficients should be equal.

## 7. The solution to the system of equations x – y = 4 and x + y = 2 is:

### Answer:

### Explanation:

Solving the equations simultaneously, we get x = 3 and y = -1.

## 8. Which of the following pairs of equations are parallel?

### Answer:

### Explanation:

The lines have the same slope but different y-intercepts, hence they are parallel.

## 9. If a system of two equations has a unique solution, then the lines are:

### Answer:

### Explanation:

If there's a unique solution, the two lines intersect at just one point.

## 10. The system of equations 2x – y = 3 and 4x – 2y = 6 has:

### Answer:

### Explanation:

Both equations represent parallel lines as they have the same slope.

## 11. The graph of the equation 3x – 4y = 12 intersects the x-axis at:

### Answer:

### Explanation:

Setting y = 0 in the equation, we get x = 4.

## 12. The solution to the system of equations x + y = 5 and x – y = 1 is:

### Answer:

### Explanation:

Solving the equations simultaneously, we get x = 3 and y = 2.

## 13. If the lines represented by the equations 2x + 3y = 5 and ax + by = 7 are parallel, then:

### Answer:

### Explanation:

Parallel lines have the same slope. Thus, a/b should be equal to the ratio of the coefficients of x and y in the first equation.

## 14. If the pair of equations x – y = 2 and cx – dy = 2 has no solution, then:

### Answer:

### Explanation:

For no solution, the lines should be parallel. Thus, the ratio of coefficients should be the same.

## 15. The system of equations 3x – 2y = 8 and 6x – 4y = 16 has:

### Answer:

### Explanation:

Both equations represent the same line, leading to infinite solutions.

## 16. The condition for the lines 3x – 5y = 7 and kx – 5y = 14 to be parallel is:

### Answer:

### Explanation:

The lines are parallel if they have the same slope. Thus, k should be 6 to maintain the same ratio of x and y coefficients.

## 17. The graph of the equation y = 3 intersects the x-axis at:

### Answer:

### Explanation:

The equation represents a horizontal line passing through the point (0,3). It doesn't intersect the x-axis.

## 18. The solution of the pair of equations 2x + y = 7 and x – 2y = 3 is:

### Answer:

### Explanation:

Solving the equations simultaneously, we get x = 3 and y = 1.

## 19. If the pair of equations 2x + 3y = 6 and 4x + ky = 8 has a unique solution, then k is not equal to:

### Answer:

### Explanation:

For a unique solution, the lines should not be parallel. Therefore, k should not equal the ratio of coefficients from the first equation.

## 20. The pair of equations y = x and y = -x represents lines that are:

### Answer:

### Explanation:

The lines y = x and y = -x have slopes that are negative reciprocals of each other, hence they are perpendicular.