System of Equations Word Problems Day 1

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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 set of values that satisfy all equations in the system.

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values that satisfy all equations simultaneously.

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution to the system.

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How do you find the solution to a system of equations graphically?

Back

Plot each equation on the same graph. The point(s) where the lines intersect represent the solution(s) to the system.

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What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then 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 remaining variable.

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How can you check if your solution to a system of equations is correct?

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Substitute the solution values back into the original equations to see if they hold true.

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What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the meaning of the variables in a system of equations word problem?

Back

The variables represent unknown quantities that we are trying to find, often related to real-world scenarios.