Flashcard on Systems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Front

What does it mean if a system of equations has no solution?

Back

If a system of equations has no solution, it means that the equations represent parallel lines that never intersect.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the graphical representation of a system of equations with one solution?

Back

The graphical representation of a system of equations with one solution consists of two lines that intersect at a single point.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

Front

What is the first step in solving the system of equations 3x + 2y = 13 and y = 4x + 1?

Back

The first step is to substitute the expression for y from the second equation into the first equation.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, indicating that they will never intersect.

Front

What is the solution to the system of equations y = 4x + 1 and 3x + 2y = 13?

Back

The solution to the system is the point (1, 5), which is where the two lines intersect.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How can you tell 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 have the same slope and y-intercept.