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 linear equations to have a unique solution?

Back

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

Front

What does it mean for a system of linear equations to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of linear equations by graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the substitution method for solving systems of linear equations?

Back

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

Front

What is the elimination method for solving systems of linear equations?

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

It is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the standard form of a linear equation?

Back

It is written as Ax + By = C, where A, B, and C are integers.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if they satisfy all equations, it is a solution.