Homework 4: Systems of Equations - Word Problems

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 in the system.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What does the variable 'a' represent in the equation a + b = 100?

Back

In this context, 'a' represents the number of product A sold.

Front

What does the variable 'b' represent in the equation 15a + 25b = 2000?

Back

In this context, 'b' represents the number of product B sold.

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane. The point where the lines intersect is the solution to the system.

Front

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

Back

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

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the values of the variables that make all equations in the system true.

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How can you check if your solution to a system of equations is correct?

Back

Substitute the values of the variables back into the original equations to see if they hold true.

Front

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

Back

It means the equations represent parallel lines that never intersect, indicating that there are no values that satisfy both equations.