Systems of Equations and Inequalities 2024

Front

What is a system of equations?

Back

A system of equations is a set of two or more 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

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing each equation on a coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (dashed for < or >, solid for ≤ or ≥). 2. Shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between '≤' and '<'?

Back

'≤' means less than or equal to, including the boundary. '<' means strictly less than, excluding the boundary.

Tags

CCSS.6.EE.B.8

Front

What is the substitution method for solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

Back

The elimination method 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