Solving Systems 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 a system of equations has no solution?

Back

It means that the lines representing the equations are parallel and never intersect.

Front

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

Back

It means that the lines intersect at exactly one point.

Front

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

Back

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

Front

How can you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

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

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and write them together.

Front

What is the graphical representation of the equation y = mx + b?

Back

It represents a straight line where m is the slope and b is the y-intercept.