Linear Equations (Number of Solutions and translating Equations)

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 for a linear equation to have one solution?

Back

A linear equation has one solution when the graph of the equation intersects the x-axis at exactly one point.

Front

What does it mean for a linear equation to have infinite solutions?

Back

A linear equation has infinite solutions when the two sides of the equation are equivalent for all values of the variable, resulting in the same line when graphed.

Front

What does it mean for a linear equation to have no solution?

Back

A linear equation has no solution when the two sides of the equation represent parallel lines that never intersect.

Front

How do you create an equation with one solution?

Back

To create an equation with one solution, ensure that the coefficients of the variable on both sides are different.

Front

How do you create an equation with infinite solutions?

Back

To create an equation with infinite solutions, make both sides of the equation identical after simplification.

Front

How do you create an equation with no solution?

Back

To create an equation with no solution, set the two sides of the equation to be equal but with different constant terms.

Front

Translate: The sum of a number and 5 equals 10.

Back

x + 5 = 10

Front

Translate: Four times a number decreased by 3 is equal to 9.

Back

4x - 3 = 9

Front

What is the solution to the equation 2x + 3 = 11?

Back

x = 4