Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) 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 linear equations?

Back

To solve a system of linear equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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 remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you represent a linear equation in slope-intercept form?

Back

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation of a system of linear equations consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) of the system.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that the system has no solution.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines coincide in a system of equations?

Back

If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

Tags

CCSS.8.EE.C.8A

Front

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

Back

To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in using the substitution method?

Back

The first step in using the substitution method is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6