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 if a system of equations has one solution?

Back

The lines represented by the equations intersect at exactly one point.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The lines represented by the equations coincide, meaning they are the same line.

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

How do you solve a system of equations using elimination?

Back

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

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 solution to the system of equations: 3x + y = -14 and -2x - y = 9?

Back

(-5, 1)

Front

What is the solution to the system of equations: -2x + y = 10 and 4x - y = -14?

Back

(-2, 6)

Front

If two lines intersect at one point, how many solutions does the system have?

Back

One solution.