ACT Math Linear Equations Flashcard

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

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

Back

A system of linear equations is consistent if there is at least one solution that satisfies all equations in the system.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

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

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the elimination method for solving systems of linear equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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

What is the point of intersection of two lines?

Back

The point of intersection is the solution to the system of equations represented by the two lines, where they meet on the graph.

Front

What does it mean if two lines are parallel in terms of their equations?

Back

If two lines are parallel, their equations have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the significance of the determinant in a system of linear equations?

Back

The determinant helps determine whether a system of equations has a unique solution, no solution, or infinitely many solutions.

Front

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

Back

To check if a solution is correct, substitute the values of the variables back into the original equations to see if they hold true.