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 equations to have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line.

Front

How do you represent a system of equations graphically?

Back

By plotting the lines of each equation on the same coordinate plane.

Front

What is the substitution method in solving linear systems?

Back

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

Front

What is the elimination method in solving linear systems?

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

Front

What is the point of intersection in a linear system?

Back

The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.

Front

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

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By substituting the solution back into the original equations to see if they hold true.

Front

What is the standard form of a linear equation?

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The standard form is Ax + By = C, where A, B, and C are integers, and A is non-negative.