Solving Systems by Substitution (easy)

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to eliminate a variable in a system of equations?

Back

Eliminating a variable means manipulating the equations so that one variable is removed, allowing for the solution of the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you add two equations together in a system?

Back

To add two equations, align them vertically and add the corresponding sides together, combining like terms.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point (x, y) where the two equations intersect, representing the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in using the substitution method?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values back into the original equations to see if both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What happens when two equations represent parallel lines?

Back

When two equations represent parallel lines, they have no solution because they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients determine the slope and position of the lines represented by the equations, affecting whether they intersect, are parallel, or are the same line.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation by itself.

Tags

CCSS.6.EE.B.7