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 graphical method for solving systems of equations?

Back

Plotting each equation on a graph and identifying the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is substitution in the context of 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 elimination in the context of solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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

How do you determine the solution of a system of equations graphically?

Back

By finding the intersection point(s) of the graphs of the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system: y = 4x + 1 and 3x + 2y = 13?

Back

(1, 5) - This is the point where both equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve the system using substitution: x = -3 and 2x + 3y = 6?

Back

Substituting x = -3 into the second equation gives y = 4, so the solution is (-3, 4).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6