Systems (Substituting Points)

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

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

How do you determine if a point is a solution to an equation?

Back

To determine if a point is a solution, substitute the x and y values of the point into the equation and check if the equation holds true.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations on a coordinate plane.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

Front

What does it mean if two lines coincide in a system of equations?

Back

If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves; a positive slope rises, while a negative slope falls.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you tell if a point is a solution to both equations in a system?

Back

A point is a solution to both equations if substituting its coordinates satisfies both equations.