Systems Word Problems

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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear 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 express them in a standard form.

Front

What does it mean when two equations in a system have the same solution?

Back

It means that the two equations represent the same line on a graph, and thus, they intersect at every point along that line.

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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.

Front

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

Back

Substitute the values of the variables back into the original equations to see if they satisfy both equations.

Front

What is a linear equation?

Back

A linear equation is an equation that makes 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.

Front

What is the significance of the coefficients in a linear equation?

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Coefficients represent the rate of change of the dependent variable with respect to the independent variable in a linear equation.

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How do you interpret the solution of a system of equations graphically?

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The solution is the point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What is a word problem?

Back

A word problem is a mathematical problem presented in a narrative form, requiring interpretation and translation into mathematical expressions.