TEKS A.2I: Writing Systems of Equations

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What is a system of equations?

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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.

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How can you represent a system of equations graphically?

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

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

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A consistent system of equations has at least one solution. This can be either one unique solution (intersecting lines) or infinitely many solutions (coincident lines).

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

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An inconsistent system of equations has no solutions. This occurs when the lines represented by the equations are parallel and never intersect.

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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.

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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.

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What is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) of intersection, which represent the solution(s) to the system.

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

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How do you find the slope of a line given two points?

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What is the meaning of the y-intercept in a linear equation?

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