Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean if a linear system has 0 solutions?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a linear system has 1 solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean if a linear system has infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line.

Front

How do you solve a system of linear equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope is 2.

Front

What is the y-intercept of the line represented by the equation y = 4x - 1?

Back

The y-intercept is -1.

Front

How do you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept, then use the slope to find another point.