Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method?

Back

A technique for solving systems of equations by removing one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical interpretation of a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

They determine the slope and position of the lines represented by the equations.

Tags

CCSS.8.EE.C.8A

Front

How do you multiply an equation by a constant in elimination?

Back

You can multiply one or both equations by a constant to align coefficients for elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6