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 is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for two lines to intersect?

Back

Two lines intersect when they share a common point, which is the solution to the system of equations represented by those lines.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The solution can be determined by graphing the equations and identifying the point where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The coordinates (x, y) represent the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, they do not intersect, meaning there is no solution to the system of equations.

Tags

CCSS.8.EE.C.8B

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 between two points on the line.

Tags

CCSS.8.EE.B.5

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

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) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.