Unit 6: Solving Systems of Equations Review

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What is a system of equations?

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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 system of equations graphically?

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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).

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

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A system of equations has no solution if the lines representing the equations are parallel, meaning they never intersect.

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

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A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you solve a system of equations using substitution?

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To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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To solve using elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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

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The slope indicates the steepness of the line and the direction it goes (positive slope goes up, negative slope goes down).

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How can you determine the cost of an item from a system of equations?

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You can determine the cost of an item by solving the system of equations that represents the total costs of different combinations of items.

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What is the first step in solving a word problem involving a system of equations?

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The first step is to define the variables that represent the unknown quantities in the problem.