TEKS A.2I: Writing Systems of Equations

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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 set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you represent a system of equations graphically?

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A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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CCSS.8.EE.C.8B

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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).

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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. This occurs when the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting 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 elimination method for solving systems of equations?

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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

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How do you write a system of equations from a word problem?

Back

To write a system of equations from a word problem, identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

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What is the importance of coefficients in a system of equations?

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Coefficients represent the relationship between variables in an equation. They determine the slope of the line when graphed and affect the solution of the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the meaning of the slope in a linear equation?

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The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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CCSS.8.EE.B.5