Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for two lines to be parallel in the context of linear equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

How can you solve a system of linear equations using the substitution method?

Back

To solve using substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphical representation of a solution to a system of linear equations?

Back

The solution is represented by the point where the lines intersect on a graph.

Front

What is the elimination method for solving systems of linear equations?

Back

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

Front

What does it mean if a system of linear equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they never intersect.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine the slope of a line from its equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation y = 2/3x - 2?

Back

The slope of the line is 2/3.

Front

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

Back

The y-intercept can be found by setting x = 0 in the equation and solving for y.