Systems of Equations (All three methods)

Front

What does it mean if a system of linear equations has one solution?

Back

The two lines are intersecting lines.

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute.

Front

Write the equation for the total cost (C) of towing a vehicle for m miles if the service center charges a flat fee of $50 plus $8 per mile.

Back

C = 8m + 50

Front

How many solutions does a system of equations have if the lines are the same?

Back

Infinitely Many Solutions.

Front

What is the value of the y-coordinate of the solution to the system of equations x - 2y = 1 and x + 4y = 7?

Back

1

Front

What are the three methods to solve a system of equations?

Back

Graphing, Substitution, and Elimination.

Front

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

Back

The system has no solution.

Front

If a system of equations has infinitely many solutions, what can be said about the two lines?

Back

They are the same line.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable.