Solve Systems of 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

How do you represent a real-world problem as a system of equations?

Back

Identify the variables, formulate equations based on the relationships described in the problem, and ensure the equations reflect the constraints and conditions given.

Tags

CCSS.HSA.CED.A.3

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves plotting the equations on a graph and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

You can check the solution by substituting the values back into the original equations to see if they satisfy all equations.

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 represent the relationship between the variables in the equations, indicating how much one variable affects the other.

Tags

CCSS.8.EE.C.8B

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2