Solving Systems of Linear Equations

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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 equations by elimination?

Back

Solving by elimination 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

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 graphical interpretation of a system of linear equations?

Back

The graphical interpretation involves plotting the equations on a graph; the solution is the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinite solutions?

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the slopes and intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

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 other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method's first step?

Back

The first step is to align the equations and manipulate them (by multiplying if necessary) to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system of equations by elimination: -x + y = -13 and -8x - 4y = -8.

Back

(5, -8)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6