Equal Values Method

Front

What is the Equal Values Method in solving systems of equations?

Back

The Equal Values Method involves setting two equations equal to each other to find the point where they intersect, which represents the solution to the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a system of equations has no solution using the Equal Values Method?

Back

A system has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.C.8B

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

Given the equations y = 2x + 3 and y = 2x - 1, what can you conclude about their solutions?

Back

The system has no solution because the lines are parallel (same slope, different y-intercepts).

Tags

CCSS.8.EE.C.8B

Front

How do you solve the system of equations y = 3x + 2 and y = 5x - 4 using the Equal Values Method?

Back

Set the equations equal: 3x + 2 = 5x - 4. Solve for x to find the solution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in using the Equal Values Method?

Back

The first step is to set the two equations equal to each other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If you have the equations y = x + 1 and y = -x + 5, how do you find the solution?

Back

Set x + 1 = -x + 5, solve for x, then substitute back to find y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the solution (2, 3) represent in the context of a system of equations?

Back

It represents the point where the two lines intersect, meaning both equations are satisfied at this point.

Tags

CCSS.8.EE.C.8B

Front

How can you verify the solution of a system of equations?

Back

Substitute the solution back into both original equations to check if both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the slopes of two lines in a system of equations?

Back

The slopes determine the relationship between the lines: if they are equal, the lines are parallel; if they are different, they will intersect at one point.

Tags

CCSS.8.EE.C.8B