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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8A

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.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The solution is (2, 1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.HSA.CED.A.3

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8C

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.

Tags

CCSS.8.EE.C.8C