Solving 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

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

Front

What is substitution 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 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

How do you represent the cost of a pizza with toppings as a linear equation?

Back

Cost = Base Price + (Cost per topping * Number of toppings). For example, y = 6.80 + 0.90x.

Front

What is the solution to the system: y = -3x + 4 and x = 3?

Back

(3, -5) - Substitute x into the first equation to find y.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the lines intersect on a graph.