Solving Systems of Equations

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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 into equations, and express the conditions given in the problem.

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What does it mean if a system of equations has one solution?

Back

It means the lines represented by the equations intersect at exactly one point, indicating a unique solution for the variables.

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

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It means the lines represented by the equations are parallel and never intersect, indicating that there is no set of values for the variables that satisfies both equations.

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

Back

It means the lines represented by the equations coincide, or are the same line, indicating that there are an infinite number of points that satisfy both equations.

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How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

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How do you solve a system of equations using elimination?

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Add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the perimeter of a rectangle?

Back

The perimeter is the total distance around the rectangle, calculated as P = 2(length + width).

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If the length of a rectangle is 4 more than its width, how can you express this relationship?

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If w is the width, then the length can be expressed as l = w + 4.

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What is the first step in solving the system of equations m + c = 55 and m - c = 3?

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You can use either substitution or elimination. A common first step is to solve one equation for one variable.