Solving 3-variable systems REVIEW

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 a 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 interpretation of a system of equations?

Back

The solutions to a system of equations can be represented as the points where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a unique solution in a system of equations?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is an infinite solution in a system of equations?

Back

Infinite solutions occur when the equations represent the same line, meaning there are countless points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is no solution in a system of equations?

Back

No solution occurs when the lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

How do you represent a system of equations algebraically?

Back

A system of equations can be represented in the form: 1. ax + by = c 2. dx + ey = f 3. gx + hy = i, where a, b, c, d, e, f, g, h, i are constants.

Tags

CCSS.HSA.REI.C.8

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations so that like terms are in the same column, making it easier to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations by substitution?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6