Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean if a system of linear equations has one solution?

Back

Only one set of values for the variables satisfies all equations in the system.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What is the definition of no solution in a system of linear equations?

Back

The equations represent parallel lines that never intersect.

Front

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

Back

(3, 1)

Front

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

Back

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

Front

What is the solution to the system of equations: 3x + 2y = 12 and 6x + 4y = 24?

Back

Infinitely many solutions.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the intersection of two lines graphically?

Back

Plot both lines on a graph and identify the point where they cross.