Linear Equations and Their Solutions

This video tutorial explains how to find solutions to linear equations in two variables. It covers two methods: choosing values for x and solving for y, and setting x or y to zero to find solutions. The tutorial demonstrates these methods with examples, emphasizing that linear equations have infinitely many solutions. The video concludes with a summary and encourages viewers to explore further solutions.

What is a characteristic of linear equations in two variables?

• They have no solutions.

• They have a single solution.

• They have exactly two solutions.

• They have infinitely many solutions.

What is the first step in finding a solution to a linear equation?

• Graph the equation.

• Choose a value for one variable.

• Choose a value for both variables.

• Solve for both variables simultaneously.

When y is isolated on one side, what is usually easier to do?

• Choose values for y and solve for x.

• Eliminate y from the equation.

• Choose values for x and solve for y.

• Graph the equation.

What is the ordered pair solution when x = -1?

• (-1, 5)

• (-1, 0)

• (-1, 2)

• (-1, 7)

What is the ordered pair solution when x = 0?

• (0, 2)

• (0, 5)

• (0, 7)

• (0, 0)

What is the ordered pair solution when x = 2?

• (2, 8)

• (2, 2)

• (2, -8)

• (2, 0)

How can more solutions to a linear equation be found?

• By solving for both variables simultaneously.

• By substituting any value for x or y.

• By graphing the equation.

• By eliminating one variable.

What is a strategy for finding solutions when both variables are on the same side?

• Neither A nor B.

• Both A and B.

• Set y = 0 and solve for x.

• Set x = 0 and solve for y.

What is the ordered pair solution when x = 0 in the second example?

• (0, 0)

• (0, 3)

• (0, 4)

• (0, 1)

What is the ordered pair solution when y = 0 in the second example?

• (0, 0)

• (3, 0)

• (4, 0)

• (1, 0)