Determining Solutions for Systems of Equations

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 system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

Substitute the ordered pair into each equation; if it satisfies all equations, it is a solution.

Front

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

Back

The system has no solutions because the lines never intersect.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a coordinate plane.

Front

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

Back

(1, 3) is the solution.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute 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 for the other.

Front

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

Back

It represents the solution to the system, where both equations are satisfied.