Systems of equations and inequalities

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 linear equations graphically?

Back

To solve a system of linear equations graphically, plot each equation on the same coordinate plane and identify 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 of equations has no solution if the lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method for 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 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 variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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 on a graph.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the difference between '>' and '≥' in inequalities?

Back

The symbol '>' indicates that one value is greater than another, while '≥' indicates that one value is greater than or equal to another.

Tags

CCSS.6.EE.B.8

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8A