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 to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

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 is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3)

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

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

What is the graphical representation of the solution (3, 0)?

Back

It is the point where the x-coordinate is 3 and the y-coordinate is 0 on a Cartesian plane.

Front

If Joe bought 10 cups of coffee and 5 doughnuts for $16.50, what equation represents this situation?

Back

10c + 5d = 16.50, where c is the cost of coffee and d is the cost of doughnuts.

Front

What is the first step in solving the system of equations 2x + 3y = 6 and x - y = 2?

Back

You can use either substitution or elimination; for substitution, solve one equation for one variable.