systems equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system with an infinite number of solutions?

Back

The graphical representation of a system with an infinite number of solutions is when the equations represent the same line, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

You can determine this by analyzing the slopes and intercepts of the lines represented by the equations. If the slopes are different, there is one solution; if they are the same but different intercepts, there is no solution; if they are the same and the same intercept, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations 3x + 7y = 23 and -3x - 7y = -17?

Back

The solution is no solution, as the two equations represent parallel lines.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, resulting in an infinite number of solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations -4x - 2y = -12 and 4x + 8y = -24?

Back

The solution is (6, -6).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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 the number of solutions.

Tags

CCSS.8.EE.C.8B

Front

How can you use substitution to solve a system of equations?

Back

You can solve a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6