8.9A Simultaneously Satisfies

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 for two equations to intersect?

Back

It means they have at least one solution in common, represented by the point of intersection on a graph.

Front

What is the solution to a system of equations?

Back

The point where the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

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

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How do you solve a system of equations using substitution?

Back

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

Front

How do you solve a system of equations using elimination?

Back

You add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the point of intersection for the equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the point of intersection.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.