System 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 for a system of equations to have one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the graphs of the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so they intersect at every point on that line.

Front

How do you solve a system of equations using substitution?

Back

You solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

You add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is a zero pair in the context of systems of equations?

Back

A zero pair occurs when two terms cancel each other out, allowing for easier solving of the equations.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where their intersections represent solutions.

Front

What is the first step in solving the system: 2x - 3y = -1 and y = x - 1?

Back

Substitute y = x - 1 into the first equation to solve for x.

Front

What is the solution to the system: 5x - 3y = -36 and 2x + 3y = 15?

Back

The solution is (-3, 7).