Writing Systems of Equations from Word Problems

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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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Identify the variables, translate the relationships and conditions described in the problem into equations, and ensure 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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To solve a system of equations graphically means to plot the equations on a coordinate plane and find the point(s) where the lines intersect, which represent the solution(s) to the system.

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What is the substitution method in 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 values of the variables.

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What is the elimination method in 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 can you check the solution of a system of equations?

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You can check the solution by substituting the values of the variables back into the original equations to see if they satisfy all equations.

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What is a linear equation?

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A linear equation is an equation that represents a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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

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The coefficients represent the relationship between the variables in the equations. They indicate how much one variable changes in relation to another.

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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 solution, meaning the equations represent parallel lines that never intersect.