System of Equations Review

Front

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 simultaneously.

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How do you represent a system of equations graphically?

Back

A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

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What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solution. This occurs when the equations represent parallel lines that never intersect.

Front

What is the substitution method for solving a system 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 a system of equations?

Back

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 do you find the area of a rectangle given its perimeter?

Back

To find the area of a rectangle, use the formula: Area = length × width. If the perimeter is given, use the formula: Perimeter = 2(length + width) to find the dimensions.

Front

What is the formula for the perimeter of a rectangle?

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The formula for the perimeter of a rectangle is: Perimeter = 2(length + width).

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How do you set up a system of equations from a word problem?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure the equations represent the same situation.

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What is the cost of left-handed and right-handed gloves if left-handed gloves cost $52 and right-handed gloves cost $45?

Back

Let x be the number of left-handed gloves and y be the number of right-handed gloves. The cost equation is: 52x + 45y = total cost.