2.1 Systems of Equations in Two Variables

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the lines represented by the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines on a coordinate plane, which represents the solution(s) of the system.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Front

How do you solve a system of equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the solution to the system: x - 4y = 16 and 5x + 4y = 8?

Back

(4, -3)

Front

What is the solution to the system: 7x - 2y = 6 and x - 2y = -6?

Back

(2, 4)

Front

What is the solution to the system: x + y = 3 and 3x - y = 1?

Back

(1, 2)

Front

What is the solution to the system: x + 2y = -4 and x - 2y = 8?

Back

(2, -3)