Systems of Equations - 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 represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other based on the problem's context.

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What does it mean for two companies to charge the same amount?

Back

It means that the total cost equations for both companies are equal, allowing us to set up a system of equations to find the number of items (like toppings or shirts) that make the costs equal.

Front

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

Back

Plot both equations on a graph. The point where they intersect is the solution to the system.

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What is the substitution method in 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 in solving systems of equations?

Back

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 a linear equation?

Back

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

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What does 'x' and 'y' typically represent in word problems?

Back

In word problems, 'x' and 'y' usually represent unknown quantities that we need to find.

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

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

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

Back

Coefficients represent the rate of change or the relationship between the variables in the equations.