Systems of Equations -graphing & substitution

Front

What is the solution (x, y) to a system of equations?

Back

The point where the equations intersect.

Front

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

Back

The lines are parallel and do not intersect.

Front

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

Back

The equations represent the same line.

Front

How can you determine if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for a variable and substituting that value into the other equation.

Front

What is the graph of the equations 8x + 4y = 12 and y = -2x + 3?

Back

They intersect, indicating infinitely many solutions.

Front

How do you find the y-coordinate of the solution to the system x - 2y = 1 and x + 4y = 7?

Back

By solving the equations simultaneously, the y-coordinate is 1.

Front

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

Back

They lie on top of each other and have infinitely many solutions.

Front

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

Back

It represents the solution to the system.