Systems of Linear Equations

Front

What is the solution of a system of linear equations?

Back

The solution is the intersection of the two equations on a graph.

Front

What is the substitution method in solving systems of linear equations?

Back

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

Front

How do you solve the system of equations y=3x+14 and y=-4x by substitution?

Back

Set 3x + 14 = -4x, solve for x, then substitute back to find y. The solution is y = -2.

Front

What does it mean if a system of linear equations has an infinite number of solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

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

Back

The graphical method involves plotting both equations on a graph and identifying their intersection point.

Front

What is the solution to the system of equations y=5x+3 and y=-2x-4 when solved by graphing?

Back

The solution is the point (-1, -2).

Front

What does it mean if two lines are parallel in the context of linear equations?

Back

If two lines are parallel, it means they have no points of intersection and thus no solutions.

Front

What is the standard form of a linear equation?

Back

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

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

Front

What is the elimination method in 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.