ALB M1 Solving 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 if a system of linear equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinite solutions?

Back

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

Front

How do you solve a system of equations using substitution?

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 elimination?

Back

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

Front

What is the graphical representation of a system of linear equations?

Back

The solution is the point(s) where the lines intersect on a graph.

Front

What is the solution to the system: 3x + y = 1 and y = 4x + 1?

Back

(0, 1)

Front

What is the solution to the system: 7x - 9y = 29 and 7x + 2y = -15?

Back

(-1, -4)

Front

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

Back

The lines intersect at exactly one point.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations so that corresponding variables and constants are in the same columns.