Linear Systems Alg/Gr

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How do you solve a system of equations using the substitution method?

Back

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

Front

How do you solve a system of equations using the elimination method?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of intersecting lines?

Back

Intersecting lines represent a system of equations with a unique solution.

Front

What is the graphical representation of parallel lines?

Back

Parallel lines represent a system of equations with no solution.

Front

What is the graphical representation of the same line?

Back

The same line represents a system of equations with infinite solutions.

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

Back

(3, 0) is the solution.

Front

Solve the system: 3x - 2y = 4 and 6x - 4y = 8.

Back

Infinite solutions, as the second equation is a multiple of the first.