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 for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing the equations.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

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

Back

If the lines are parallel, they have the same slope but different y-intercepts, indicating no intersection.

Front

What is the elimination method for solving systems of equations?

Back

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

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

What is the first step in solving the system: 3x - y = 7 and 2x + y = 3?

Back

You can use either substitution or elimination; for elimination, add the equations to eliminate y.

Front

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

Back

Coefficients represent the rate of change of the variables in the equations.