## Questions and Answers

Which of the following statements is true about a pair of linear equations in two variables?

All of the above

What is the graphical representation of a pair of linear equations in two variables that have a unique solution?

Intersecting lines

What is the condition for a pair of linear equations in two variables to have no solution?

The lines are parallel

Quina és la solució del sistema d'equacions següent? x + y = 5 2x - y = 3

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Quina és la condició perquè un sistema d'equacions lineals en dues variables tingui una infinida solució?

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Quina és la solució del sistema d'equacions següent? 3x - 4y = 2 6x - 8y = 4

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Which of the following is NOT a method to solve a pair of linear equations in two variables?

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What is the solution of the pair of linear equations 3x - 2y = 7 and 2x + y = 4?

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What is the condition for a pair of linear equations in two variables to have infinitely many solutions?

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## Study Notes

### Pair of Linear Equations in Two Variables

- A pair of linear equations in two variables can have a unique solution, no solution, or infinitely many solutions.

### Graphical Representation

- The graphical representation of a pair of linear equations in two variables with a unique solution is two intersecting lines.

### Condition for No Solution

- The condition for a pair of linear equations in two variables to have no solution is that the two lines are parallel and do not intersect.

### Solving Systems of Equations

- The solution to the system of equations x + y = 5 and 2x - y = 3 is x = 2 and y = 3.

### Condition for Infinitely Many Solutions

- The condition for a pair of linear equations in two variables to have infinitely many solutions is that the two lines coincide.

### Solving Another System of Equations

- The solution to the system of equations 3x - 4y = 2 and 6x - 8y = 4 is no solution, as the lines are parallel and do not intersect.

### Methods to Solve a Pair of Linear Equations

- The methods to solve a pair of linear equations in two variables are substitution, elimination, and graphical method.
- Guessing is NOT a method to solve a pair of linear equations in two variables.

### Solving Another System of Equations

- The solution to the system of equations 3x - 2y = 7 and 2x + y = 4 is x = 3 and y = 1.

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