Solving 3-variable systems REVIEW

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the points where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by elimination?

Back

Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by substitution?

Back

Substitution involves solving one equation for one variable and then substituting that expression into another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines or planes represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is a unique solution in a system of equations?

Back

A unique solution occurs when the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is no solution in a system of equations?

Back

No solution occurs when the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is infinitely many solutions in a system of equations?

Back

Infinitely many solutions occur when the equations represent the same line, meaning they intersect at every point on that line.

Tags

CCSS.8.EE.C.8A

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify that all equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Coefficients determine the slope and position of the lines or planes represented by the equations.

Tags

CCSS.8.EE.C.8A

Front

What is a variable in the context of a system of equations?

Back

A variable is a symbol used to represent an unknown value in the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6