Solving Systems of Linear Equations

Front

What does it mean when two linear equations graph to the same line?

Back

It means that there are infinite solutions to the system of equations.

Tags

CCSS.8.EE.C.8A

Front

What is the definition of a solution to a system of equations?

Back

A solution is any ordered pair that makes both equations true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you identify a linear graph?

Back

A linear graph is a straight line, which represents a linear equation.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general form of a linear equation?

Back

The general 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 it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and will never intersect.

Tags

CCSS.8.EE.C.8A

Front

How do you write an equation for a real-world scenario involving costs?

Back

Identify the fixed costs and variable costs, then express the total cost as a function of the variable.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

The slope-intercept 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 is the significance of the y-intercept in a linear equation?

Back

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

Front

What does it mean for two lines to intersect at a point?

Back

It means that there is exactly one solution to the system of equations represented by those lines.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By analyzing the slopes and y-intercepts of the lines: if they are the same, there are infinite solutions; if they are parallel, there is no solution; if they intersect, there is one solution.

Tags

CCSS.8.EE.C.8B