Systems of equations

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?

Back

Finding 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

A method where one equation is solved for one variable, and that expression is substituted 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

A method where equations are added or subtracted to eliminate 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 graphically solve a system of equations?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The point(s) (x, y) where the equations intersect, representing the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines representing the equations are parallel and 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

Solve for x and y: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve using substitution: 5x - 4y = -16 and x + 2y = -6.

Back

(-4, -1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6