Substitution

Front

What is substitution in solving systems of equations?

Back

Substitution is a method used to solve systems of equations by replacing one variable with an expression derived from another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you start solving a system of equations by substitution?

Back

Identify one equation and solve for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Given the equations y = 2x + 3 and 4x - y = 1, what is the first step to solve by substitution?

Back

Substitute y in the second equation: 4x - (2x + 3) = 1.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean to isolate a variable?

Back

To isolate a variable means to manipulate an equation so that the variable is on one side of the equation by itself.

Front

If y = 3x + 2, how can you substitute y in the equation 2x + y = 10?

Back

Replace y with 3x + 2: 2x + (3x + 2) = 10.

Front

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

Back

Set the equations equal to each other: 2x + 1 = -x + 4, solve for x, then find y.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the purpose of substitution in solving equations?

Back

The purpose is to simplify the system to a single equation with one variable, making it easier to solve.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

How do you check your solution after using substitution?

Back

Substitute the values of the variables back into the original equations to verify they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a common mistake when using substitution?

Back

A common mistake is incorrectly substituting or simplifying the equations, leading to wrong solutions.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Given the equations x = 2y + 1 and 3x + 2y = 12, what is the first step?

Back

Substitute x in the second equation: 3(2y + 1) + 2y = 12.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6