one solution, no solution, infinite solutions

Front

What is meant by 'one solution' in a linear equation?

Back

A linear equation has 'one solution' when the graph of the equation is a straight line that intersects the x-axis at exactly one point.

Front

What does 'no solution' indicate in a system of equations?

Back

'No solution' means that the equations represent parallel lines that never intersect, indicating that there is no point that satisfies both equations.

Front

What does 'infinite solutions' mean in the context of linear equations?

Back

'Infinite solutions' occurs when two equations represent the same line, meaning every point on the line is a solution to both equations.

Front

Solve for x: -4(3x + 2) = 3(-4x + 5)

Back

No Solution

Front

Solve for x: -5(2x - 4) = 2(10 - 5x)

Back

Infinite Solution

Front

Solve for y: 9y + 8 = 9y - 8

Back

No Solution

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

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

Back

The slope (m) indicates the steepness of the line and the direction it goes; a positive slope rises, while a negative slope falls.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

How can you determine if two lines are parallel?

Back

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