Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

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

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the graphical representation of intersecting lines?

Back

It shows that the system has one unique solution where the lines cross.

Front

What is the substitution method in 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 in 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

Solve for x and y: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

Front

Solve the system of equations: 9x - 4y = 1 and -3x + 8y = -47.

Back

(-3, -7)