NC.8.EE.8 Systems of Equations

Front

What is a system of equations?

Back

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

Front

How do you find the solution to a system of linear equations graphically?

Back

To find the solution graphically, plot both equations on the same graph and identify the point where they intersect.

Front

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

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect and have no solution.

Front

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

Back

Front

How do you determine the slope from an equation in slope-intercept form?

Back

Front

What is the y-intercept of a linear equation?

Back

Front

How can you solve a system of equations using substitution?

Back

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

Front

What is the elimination method for 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 does it mean if a system of 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

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations.