Equal Values Method Practice

Front

What is the Equal Values Method?

Back

A method used to solve systems of equations by setting the equations equal to each other to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve the system of equations y = -3x - 9 and y = 2x + 11?

Back

Set -3x - 9 = 2x + 11, solve for x to find x = -4, then substitute x back to find y = 3. Solution: (-4, 3).

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 the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to the system of equations y = 4x + 3 and y = 4x - 1?

Back

No solution, as the lines are parallel.

Tags

CCSS.8.EE.C.8B

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines; if they are the same, there are infinitely many solutions; if different, one solution; if parallel, no solution.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations y = 6x + 3 and y = 4x - 15?

Back

Set 6x + 3 = 4x - 15, solve for x to find x = -9, then substitute x back to find y = -51. Solution: (-9, -51).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

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

Tags

CCSS.8.EE.C.8A

Front

How do you graphically represent a system of equations?

Back

By plotting the lines of each equation on the same coordinate plane and observing their intersection.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Set the two equations equal to each other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Tags

CCSS.8.EE.C.8B