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.8.EE.C.8B

CCSS.HSA.REI.C.6

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 graphs intersect, which represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot each equation on the same coordinate plane and look for the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system of equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines coincide when solving a system of equations?

Back

If two lines coincide, they lie on top of each other, meaning there are infinitely many solutions to the system of equations.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the point (1, 3) in the context of a system of equations?

Back

The point (1, 3) is a solution to the system of equations, meaning that when the values x=1 and y=3 are substituted into the equations, they satisfy both equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the importance of the y-intercept in graphing linear equations?

Back

The y-intercept is the point where the line crosses the y-axis, and it is crucial for graphing linear equations as it helps determine the position of the line.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the slope of a line from its graph?

Back

The slope of a line can be determined by selecting two points on the line and using the formula: slope (m) = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope-intercept form of a linear equation is given by the formula 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