Systems of Equations

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 is the point(s) where the equations intersect.

Front

How can you solve a system of equations graphically?

Back

To solve a system of equations graphically, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

Front

What is the substitution method for 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 for 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 is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

The solution is (1, 3), where the two lines intersect.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations in the system.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which do not intersect.

Front

What is the graphical representation of the solution (2, -4)?

Back

The point (2, -4) is where the two lines of the equations intersect on the coordinate plane.