Solution to a System

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is an ordered pair (x, y) that satisfies all equations in the system.

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the x and y values of the ordered pair into each equation. If both equations are true, then the ordered pair is a solution.

Front

What does it mean if an ordered pair is not a solution to a system of equations?

Back

It means that substituting the ordered pair into at least one of the equations does not yield a true statement.

Front

Solve the system of equations: y = 2x + 3 and y = -x + 1. What is the solution?

Back

(1, 5)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Front

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

Back

If two lines are parallel, it means they have no points of intersection, and thus, there is no solution to the system.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied.

Front

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

Back

Substitute the solution back into each equation to verify that both equations hold true.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves 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

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.