Writing & 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 for a system of equations to be consistent?

Back

A system is consistent if it has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system is inconsistent if it has no solutions.

Front

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

Back

The graphs of the equations in the system, which can intersect at one point, be parallel, or coincide.

Front

What is the solution to a system of linear equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is 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 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 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 do you find the slope of a line given two points?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis (x=0).