Systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

How do you find the solution to a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.

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 no solution?

Back

It means the lines represented by the equations are parallel and do not intersect.

Front

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

Back

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

Front

Solve the system: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinitely many solutions (the second equation is a multiple of the first).

Front

Solve the system: x - y = 2 and x + y = 4.

Back

(3,1) is the solution.

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.