[b] U5D2 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 do you represent a word problem as a system of equations?

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To represent a word problem as a system of equations, identify the variables, translate the relationships and conditions described in the problem into equations, and ensure that the equations reflect the same variables.

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What does it mean to solve a system of equations graphically?

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Solving a system of equations graphically involves plotting the equations on a coordinate plane and finding the point(s) where the lines intersect, which represents the solution(s) to the system.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of the 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 significance of the coefficients in a system of equations?

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The coefficients in a system of equations represent the rate of change or the relationship between the variables. They determine the slope of the lines when graphed.

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How can you check the solution of a system of equations?

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To check the solution of a system of equations, substitute the values of the variables back into the original equations to verify that they satisfy all equations.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solution, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.