TEKS A.2I: Writing Systems of Equations

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 set of values that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you represent a linear equation in slope-intercept form?

Back

A linear equation in slope-intercept form is represented as 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

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is.

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 by the value of y when x = 0.

Front

How can you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the graphs of the equations plotted on the same coordinate plane. The point(s) where the graphs intersect represent the solution(s) of the system.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving a system of equations?

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 for solving a system of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions. The graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A