Front

What is a system of linear equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

How do you represent a word problem as a system of equations?

Back

To represent a word problem as a system of equations, identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the total quantities and values described in the problem.

Tags

CCSS.HSA.CED.A.3

Front

What does the slope of a line represent in a linear equation?

Back

The slope of a line in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. In the equation y = mx + b, 'b' represents the y-intercept.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

A system has one solution if the lines intersect at a single point, no solution if the lines are parallel (same slope, different y-intercepts), and infinitely many solutions if the lines are the same (coincident lines).

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 to find the values of both variables.

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 remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you convert a word problem into a linear equation?

Back

To convert a word problem into a linear equation, identify the quantities involved, assign variables, and translate the relationships and operations described in the problem into mathematical expressions.

Tags

CCSS.8.EE.C.7B

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation represent the rate of change of the dependent variable with respect to the independent variable. They indicate how much the dependent variable changes when the independent variable increases by one unit.

Tags

CCSS.HSF.LE.B.5

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants, and x and y are the variables.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2