Systems ACP 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 point(s) where the equations intersect.

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What does it mean to solve a system of equations using substitution?

Back

Solving a system using substitution involves solving one equation for one variable and then substituting that expression into the other equation(s) to find the values of the variables.

Front

What is the definition of a variable in mathematics?

Back

A variable is a symbol used to represent an unknown value in mathematical expressions or equations.

Front

What is the purpose of using absolute value in equations?

Back

Absolute value measures the distance of a number from zero on the number line, regardless of direction. It is used to express conditions where a value can vary within a certain range.

Front

How do you interpret the solution of a system of equations graphically?

Back

The solution of a system of equations can be interpreted as the point(s) where the graphs of the equations intersect.

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

Back

Coefficients are the numerical factors in front of variables in equations. They determine the slope and position of the lines when graphed.

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

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A system has no solution if the equations represent parallel lines that 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 has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How do you find the value of a variable in a word problem?

Back

To find the value of a variable in a word problem, translate the problem into an equation using the information given, then solve for the variable.

Front

What is the formula for calculating the total value of coins?

Back

Total value = (number of nickels * 0.05) + (number of dimes * 0.10) + (number of quarters * 0.25).