Solving Systems of Equations

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, which represents the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel?

Back

Parallel lines never intersect because they have the same slopes.

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CCSS.HSG.CO.A.1

Front

How can you determine the solution of a system of equations graphically?

Back

By graphing the equations and identifying the point of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method in 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

Front

What is the substitution method in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the two equations represent the same line.

Tags

CCSS.8.EE.C.8A

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Tags

CCSS.8.EE.B.5

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of two or more lines on a coordinate plane, where their intersections represent the solutions.

Tags

CCSS.8.EE.C.8A