EOC Review: Systems

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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 determine if a point is a solution to a system of equations?

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Substitute the coordinates of the point into each equation. If the equations are satisfied (true), then the point is a solution.

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

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The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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

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The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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What is a mixture problem in algebra?

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A mixture problem involves combining two or more substances with different properties to achieve a desired concentration or mixture.

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How do you set up a mixture problem involving percentages?

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Let x be the amount of the first substance and y be the amount of the second. Set up an equation based on the total amount and another based on the concentration.

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What is the formula for calculating the concentration of a solution?

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Concentration (%) = (Amount of solute / Total amount of solution) x 100.

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How do you solve for an unknown in a mixture problem?

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Set up an equation based on the total volume and another based on the concentration, then solve the system of equations.

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What is the relationship between wins and losses in a sports season?

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If a team wins more games than it loses, the number of wins can be expressed as the number of losses plus the difference in wins.

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How do you calculate the total number of games played if wins and losses are known?

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Total games = Wins + Losses.