Solving Systems of Linear Equations 2025

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the solution of a system of linear equations?

Back

The solution is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

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

Back

It indicates that the lines are parallel and will never intersect.

Front

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

Back

It means that the two equations represent the same line, so every point on the line is a solution.

Front

How can you determine if two lines are the same?

Back

Two lines are the same if they have the same slope and the same y-intercept.

Front

What is the substitution method in solving systems of equations?

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 systems of equations?

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 of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, found by setting x=0 in the equation of the line.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.