Solving Systems by Graphing

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 to the system is the point(s) where the equations intersect.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean to solve a system of equations by graphing?

Back

Solving a system of equations by graphing involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the set of values for the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it indicate if two lines on a graph are parallel?

Back

If two lines are parallel, it indicates that the system of equations has no solution, as the lines will never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines on a graph coincide?

Back

If two lines coincide, it means they are the same line, indicating that the system of equations has infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

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

Back

You can determine the solution graphically by finding the point of intersection of the lines representing the equations on a graph.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the coordinates (x,y) in the context of a solution to a system of equations?

Back

The coordinates (x,y) represent the values of the variables that satisfy all equations in the system, indicating the point of intersection on the graph.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line on a graph, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

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 y-intercept of a line?

Back

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