How Many Solutions??????

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when the lines represented by the equations are parallel.

Front

What is the solution to the equation 10x + 9 = 4x - 9?

Back

-3

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation. This occurs when the two sides of the equation are equivalent.

Front

What is the first step in solving a linear equation?

Back

The first step is to isolate the variable on one side of the equation by performing inverse operations.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the solution to the equation 2x + 3 = 3x - 5?

Back

8

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions can be found where the equations intersect.