Solutions to Systems of Equations & Graphing to Solve Systems

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 a point to be a solution to a system of equations?

Back

The (x,y) coordinates satisfy all equations in the system.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the (x,y) coordinates into each equation and check if they hold true.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection of lines on a graph.

Front

What does it mean if two lines in a system of equations are parallel?

Back

The system has no solution because the lines never intersect.

Front

What is the solution to a system of equations represented graphically?

Back

The point where the lines intersect.

Front

What is an example of a system of equations?

Back

2x + 3y = 6 and x - y = 2.

Front

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

Back

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

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve.