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 two lines on a graph are parallel?

Back

They have no solutions because they never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the lines intersect on a graph.

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

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 do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

Solve for x and y: y = 3x + 2 and y = -x + 4.

Back

(1, 5)

Front

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

Back

(3, 0)

Front

What is the first step in graphing a system of equations?

Back

Convert each equation to slope-intercept form (y = mx + b) if necessary.