Systems of Linear Equations (Two Variables)

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a solution to a system of linear equations to be valid?

Back

A solution is valid if it satisfies all equations in the system, making them true when the values are substituted.

Front

How is a solution to a system of linear equations represented?

Back

A solution is represented as an ordered pair (x, y), where x is the value of the first variable and y is the value of the second variable.

Tags

CCSS.HSA.REI.C.9

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of linear equations?

Back

The substitution method involves solving one equation for one variable and 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 systems of linear equations?

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

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

Back

If two lines are parallel, the system has no solution because the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines coincide in a system of linear equations?

Back

If two lines coincide, the system has infinitely many solutions because every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The slope-intercept form is 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 find the x-intercept of a linear equation?

Back

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