Solving Algebraic Word Problems with Systems of Equations

What is the first step in solving a coin problem using systems of equations?

• Define the variables

• Solve for one variable

• Graph the equations

• Check the solution

If Steve has 83 coins in total and the total value is $10.70, which of the following represents the equation for the total number of coins?

• 10D + 25Q = 83

• D - Q = 83

• 10D + 25Q = 1070

• D + Q = 83

In the coin problem, why does the teacher multiply the top equation by -10?

• To simplify the equation

• To convert the equation to standard form

• To eliminate the variable Q

• To eliminate the variable D

What is the value of Q (number of quarters) in the coin problem?

• 10

• 67

• 83

• 16

In the lunch cost problem, what do the variables x and y represent?

• x represents the cost of a salad, y represents the cost of a soup

• x represents the cost of a soup, y represents the cost of a salad

• x represents the number of salads, y represents the number of soups

• x represents the total cost, y represents the number of items

Why does the teacher not eliminate the decimals in the lunch cost problem?

• Because it would make the numbers too large

• Because the problem requires decimals

• Because it is easier to solve with decimals

• Because it is not necessary

What is the cost of a bowl of soup in the lunch cost problem?

• $3.29

• $15.45

• $21.03

• $2.79

In the substitution problem, what does the equation 126 = 2L + 2W represent?

• The perimeter of the rectangular garden

• The area of the rectangular garden

• The width of the garden

• The length of the garden

If the width of the garden is 21 feet, what is the length?

• 42 feet

• 84 feet

• 21 feet

• 63 feet

What should you do if you encounter a similar problem to the examples provided?

• Skip the problem

• Refer back to your notes

• Guess the answer

• Ask a friend