Graphing Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Tags

CCSS.8.EE.C.8B

Front

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

Back

To find the solution graphically, plot each equation on the same set of axes and identify the point(s) where the lines intersect. This point represents the solution.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel when graphing 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.

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.C.8A

Front

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

Back

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

How do you determine the slope from an equation in slope-intercept form?

Back

The slope can be determined directly from the equation in slope-intercept form (y = mx + b) as the coefficient of x (m).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

How can you solve a system of equations by substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation to find the values of both variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of the solution (1,3) for a system of equations?

Back

The point (1,3) represents the coordinates where the two lines intersect on a graph, indicating the solution to the system.

Tags

CCSS.8.EE.C.8A

Front

What does it mean to graph the same equation twice?

Back

Graphing the same equation twice results in the same line being drawn twice, which indicates that there are infinitely many solutions.

Tags

CCSS.8.EE.C.8A