Solving Systems of Equations- Substitution

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

What does it mean to solve a system of equations using substitution?

Back

Solving a system of equations using substitution involves isolating one variable in one equation and substituting that expression into the other equation.

Front

What is the first step in solving the system: 3x + 3y = 3 and y = 3x + 5?

Back

The first step is to substitute y from the second equation into the first equation: 3x + 3(3x + 5) = 3.

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, meaning they have the same slope but different y-intercepts.

Front

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

Back

A system has infinite solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

Front

What is the solution to the system: y = 3 - x and 3y + x = 5?

Back

The solution is (2, 1).

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships into equations, and set up the system based on the problem's conditions.

Front

What is the significance of isolating a variable in one equation?

Back

Isolating a variable allows you to express it in terms of the other variable, making substitution possible.

Front

In the context of ages, how would you set up a system for: Erin is 3 years younger than twice Alex's age, and their ages combined are 33?

Back

The system is: x + y = 33 (where x = Erin's age, y = Alex's age) and y = 2x - 3.

Front

What is the first equation in the system for counting animals: 50 donkeys and chickens with 174 legs?

Back

The first equation is d + c = 50, where d is the number of donkeys and c is the number of chickens.