SOE: Standard Form

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you determine if a system of equations has a unique solution?

Back

A system of equations has a unique solution if the lines represented by the equations intersect at exactly one point.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of 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 does it mean if a system of equations has infinite solutions?

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

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.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients determine the slope and position of the line represented by the equation.

Front

How do you convert an equation from standard form to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the slope of a line in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x and is calculated as the change in y divided by the change in x.