12/19/24 Do Now

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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 set of values that satisfy all equations in the system.

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How do you represent the total number of coins in a system of equations?

Back

You can represent the total number of coins with an equation like d + n = total, where d is the number of dimes and n is the number of nickels.

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What does the equation 0.10d + 0.05n = 6.60 represent?

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This equation represents the total value of the coins, where d is the number of dimes and n is the number of nickels, with their respective values.

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

Back

Identify the variables, translate the relationships and totals into equations, and ensure you have as many equations as variables.

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

Back

The first step is to express one variable in terms of the other using one of the equations.

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What does it mean to solve a system of equations graphically?

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Solving graphically means plotting the equations on a graph and finding the point(s) where they intersect, which represents the solution.

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What is substitution in the context of solving equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into another equation.

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What is elimination in the context of solving equations?

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the significance of coefficients in a system of equations?

Back

Coefficients represent the relationship between the variables and their contribution to the total in the equations.

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How do you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they hold true.