Front

What is a system of linear equations?

Back

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

Front

How do you solve a system of linear equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

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

Back

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

Front

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

Back

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

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

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

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution into both equations. If both equations are true, the solution is correct.