Illustrating Systems of Linear Equations in Two Variables

This video tutorial introduces systems of linear equations in two variables, explaining how to write and graph them. It covers the types of solutions such as intersecting, coinciding, and parallel lines, and how to determine the nature of a system by analyzing graphs. The video concludes with practice questions to reinforce understanding.

What is a linear equation in two variables?

• An equation that can be written in the form ax + by = c where a, b, and c are real numbers and a and b are not zero.

• An equation that can be written in the form ax^2 + by = c where a, b, and c are real numbers.

• An equation that can be written in the form ax + by = c where a, b, and c are integers.

• An equation that can be written in the form ax + by = c where a and b are zero.

What does a system of linear equations consist of?

• One quadratic equation

• Two or more quadratic equations

• Two or more linear equations considered together

• One linear equation

How do you write a system of linear equations?

• Using commas

• Using braces

• Using brackets

• Using parentheses

What is the solution to a system of linear equations in two variables?

• A pair of numbers that satisfies both equations

• A single number

• A single number that satisfies both equations

• A pair of numbers that satisfies one equation

What type of graph represents a system with exactly one solution?

• Parallel lines

• Coinciding lines

• Intersecting lines

• No lines

What type of system is represented by coinciding lines?

• Consistent and dependent

• Inconsistent

• None of the above

• Consistent and independent

What type of system has no solution?

• None of the above

• Consistent and dependent

• Inconsistent

• Consistent and independent

If two lines are parallel, what can be said about their solutions?

• They have no solution

• They have infinitely many solutions

• They have one solution

• They have two solutions

What is the system called if the lines intersect at exactly one point?

• Consistent and independent

• Inconsistent

• Consistent and dependent

• None of the above

What type of system has infinitely many solutions?

• None of the above

• Consistent and dependent

• Inconsistent

• Consistent and independent