Unit 3 Post Assessment Review

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥). It represents a region of the coordinate plane.

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If the sum of two numbers, a and b, is 50 and a is 10 less than b, how do you find the product of a and b?

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Let b = x. Then a = x - 10. The equations are: a + b = 50 -> (x - 10) + x = 50. Solve for x to find a and b, then calculate the product.

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A possible first step is to solve the first equation in terms of y and substitute the result into the second equation.

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What does it mean for two lines to be parallel in a system of equations?

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Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect and have no solution.

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What is the purpose of substituting in a system of equations?

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Substituting allows you to replace one variable with an expression involving another variable, simplifying the system to find the values of the variables.

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How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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

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What is the definition of a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.