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 two lines to intersect?

Back

It means they have exactly one solution, which is the point where they cross.

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 graphical representation of a system of linear equations?

Back

It is represented by lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Front

What does it mean if two lines are parallel?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are coincident?

Back

They have infinitely many solutions because they lie on top of each other.

Front

How do you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and y-intercepts of the lines: same slope and intercept = infinite solutions, same slope different intercept = no solutions, different slopes = one solution.

Front

What is the elimination method in solving systems of equations?

Back

A method where 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

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

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships into equations, and set them equal to each other.