Solving Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean for a system of linear equations to have a solution?

Back

A solution to a system of linear equations is a set of values for the variables that makes all the equations true.

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

What does it mean if two lines intersect at a point on a graph?

Back

If two lines intersect at a point, it means that the system of equations has a unique solution at that point.

Front

What is the significance of parallel lines in a system of linear equations?

Back

Parallel lines indicate that the system of equations has no solution, as the lines never intersect.

Front

What is the elimination method in solving linear systems?

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 substitution method in solving linear systems?

Back

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

Front

How can you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they are dependent.

Front

What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

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

Back

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