HA2 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 for a system of equations to have no solution?

Back

A system of equations has no solution when the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system of equations has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

How do you find the solution to a system of equations graphically?

Back

The solution to a system of equations graphically is the point where the lines representing the equations intersect.

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving linear systems?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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 determine the slope of a line from two points?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) using two points (x1, y1) and (x2, y2).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.