Solving Linear Systems Review

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 to solve a linear system?

Back

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What are the possible outcomes when solving a linear system?

Back

1. One unique solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and then 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

How can you check if a solution is correct for a linear system?

Back

You can check a solution by substituting the values back into the original equations to see if they hold true.

Front

What is the graphical method for solving linear systems?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

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 by the value of y when x = 0.