2.4 One Solution, No Solution, Infinitely Many Solutions

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 equations represent parallel lines that never intersect.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation. This typically happens when the equations represent the same line.

Front

Solve: 5.5 - x = -4.5 - x

Back

No Solution

Front

How many solutions does the equation 3(−2x − 6) = −6x − 8 have?

Back

No Solutions

Front

What is the solution to the equation 4y − 3 = − 5y − 21?

Back

y = -2

Front

How many solutions does the equation 3x − 3 = −3 + 3x have?

Back

Infinitely Many Solutions

Front

Solve: −5x + 5 − 4x = −1 − 9x

Back

No 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 y = mx + b, where m is the slope and b is the y-intercept.

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 by the value of b in the equation y = mx + b.