4B.3 Day 2 Solving System of Equation Word Problems

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What is a system of equations?

Back

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 using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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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 other variable.

Front

Define 'variable' in the context of equations.

Back

A variable is a symbol (often x, y, or z) that represents an unknown value in an equation.

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution (they intersect at one or more points).

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What does it mean for two equations to be inconsistent?

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Two equations are inconsistent if they have no solutions (they are parallel and never intersect).

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What is a word problem in mathematics?

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A word problem is a mathematical problem expressed in words rather than numbers or symbols, requiring interpretation to formulate an equation.

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How do you translate a word problem into an equation?

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Identify the variables, determine the relationships described in the problem, and write an equation that represents those relationships.

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What is the importance of units in word problems?

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Units help clarify what quantities are being measured and ensure that calculations are consistent and meaningful.

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How do you check your solution in a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.