Systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

The slopes of parallel lines are the same.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel and have different slopes, the system has no solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

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

If a system of equations has infinitely many solutions, what does that imply about the lines?

Back

The lines are coincident, meaning they lie on top of each 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 x-intercept of a linear equation?

Back

Set y = 0 in the equation and solve for x.