Systems Substitution Method

Front

What is the substitution method in solving systems of equations?

Back

The substitution method is a technique used to solve systems of equations by solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean for an equation to be 'solved'?

Back

An equation is considered 'solved' when it has been manipulated to express one variable in terms of the other variables, allowing for substitution.

Front

How do you identify a solved equation in a system?

Back

A solved equation will have one variable isolated on one side of the equation, making it easy to substitute into another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in the substitution method?

Back

The first step is to solve one of the equations for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If you have the equations y = 2x + 3 and 3x + 2y = 12, how would you use substitution?

Back

Substitute y from the first equation into the second equation: 3x + 2(2x + 3) = 12.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations y = 2x + 3 and 3x + 2y = 12?

Back

The solution is (2, 7), found by solving the equations using substitution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a key advantage of the substitution method?

Back

A key advantage is that it can simplify the process of solving systems, especially when one equation is already solved for a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What should you do if both equations in a system are not easily solvable for one variable?

Back

You may need to manipulate one or both equations to isolate a variable before using substitution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the importance of checking your solution after using the substitution method?

Back

Checking your solution ensures that the values satisfy both original equations, confirming that the solution is correct.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means that the lines represented by the equations are parallel and do not intersect.

Tags

CCSS.8.EE.C.8A