Systems of equations review

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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 equations intersect.

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How do you solve a system of equations graphically?

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To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect. This point is the solution.

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

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A consistent system has at least one solution, meaning the lines 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 has no solutions, meaning the lines 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 substituting that expression into the other equation.

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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 other.

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What is the solution to the system: x - y = 11 and 2x + y = 19?

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(10, -1)

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How can you represent a word problem as a system of equations?

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Identify the variables, translate the relationships into equations, and set up the system based on the problem's conditions.

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

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Coefficients represent the rate of change or the weight of each variable in the equations.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.