M8 7.1-7.2 Solving 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 intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

The lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

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

Back

The lines coincide, meaning they are the same line and have an infinite number of points in common.

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 2x - y = 4 and y = -2x + 8?

Back

(3, 0) is the solution.

Front

What is the solution to the system of equations 6x + 2y = -20 and y = -2x - 4?

Back

(-6, 8) is the solution.

Front

What is the solution to the system of equations y = 2/3x - 2 and y = -x + 3?

Back

(3, 0) is the solution.