Solving Linear Systems by Graphing

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a linear system by graphing?

Back

To solve a linear system by graphing means to plot the equations on a graph and identify the point(s) where they intersect, which represents 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 makes all equations true, often represented as an ordered pair (x, y).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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 in a linear system?

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

How can you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method in solving linear systems?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving linear systems?

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

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.