System Of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean if two equations in a system have the same slope but different y-intercepts?

Back

The system has no solution because the lines are parallel and will never intersect.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What does it mean if two equations in a system are exactly the same?

Back

The system has infinitely many solutions because every point on the line is a solution.

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.

Front

What is a unique solution in a system of equations?

Back

A unique solution occurs when the two lines intersect at exactly one point.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x=0.

Front

What is the slope of a line?

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel (same slope, different y-intercepts), the system has no solution.