System Of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean when a system of equations has one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

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

Back

It means the equations represent the same line, overlapping each other.

Front

What is the graphical representation of a system with no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

How do you solve a system of equations using the substitution method?

Back

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

Front

How do you solve a system of equations using the elimination method?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the solution to the system of equations x + 4y = -3 and x + 7y = -12?

Back

(9, -3)

Front

What is the value of x + y if x = 9 and y = 5?

Back

14

Front

What does it indicate if two equations are equivalent?

Back

They have the same solution set.

Front

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

Back

It helps determine whether a system has a unique solution, no solution, or infinitely many solutions.