*Algebra Test* - Solving 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 one 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 no solution?

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 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 by substitution?

Back

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

Front

How do you solve a system of linear equations by elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

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

Back

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

Front

How do you find the slope of a line given two points?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).