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 point(s) where the graphs of the equations intersect.

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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 a 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, meaning the graphs of the equations intersect at one or more points.

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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, meaning the graphs of 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 solution.

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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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How do you determine the number of solutions in a system of linear equations?

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If the lines intersect at one point, there is one solution. If the lines are parallel, there are no solutions. If the lines coincide, there are infinitely many solutions.

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

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How can you convert standard form to slope-intercept form?

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

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