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 is the set of values that satisfy all equations in the system.

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

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A linear equation in slope-intercept form is represented as y = mx + b, where m is the slope and b is the y-intercept.

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What does the slope of a line represent?

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

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What is the y-intercept of a line?

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The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

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

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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.

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What is the graphical representation of a system of equations?

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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.

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What is the substitution method for solving a system 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.

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What is the elimination method for solving a system 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 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. It can be either independent (one solution) or dependent (infinitely many solutions).

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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. The graphs of the equations are parallel and never intersect.