4.2.6 Flashcard Review: Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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 the graphical representation of a linear equation?

Back

A straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

How do you find the solution to a system of equations graphically?

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 substitution method for 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 for 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

What is the slope-intercept form of a linear equation?

Back

The form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.