SLE - Writing and Solving Systems of Equations (Lesson)

Writing and Solving Systems of Equations

The purpose of learning how to solve systems of equations is to be able to solve real-world situations. So let us practice a few:

Three pizzas and four sandwiches cost $69. Three pizzas and seven sandwiches cost $87. How much does a pizza cost? A sandwich?

Step 1: Identify your variables.

Since there are two items of interest here, pizza and sandwiches, let p = cost of pizza and s = cost of a sandwich

Step 2: Set up your equations:

3p + 4s = 69

3p + 7s = 87

Step 3: Solve your system using any method:

Since the leading coefficients of p are similar, let us use elimination and multiply the bottom equation by -1.

3p + 4s = 69

+-3p - 7s = -87

-3s = -18

s = 6

3p +4(6)=69

3p + 24 =69

3p = 45

p = 15

Step 4: Check your answers:

3p + 4s = 69

3(15) + 4(6) = 69

45 + 24 = 69

69 = 69

3p + 7s = 87

3(15) + 7(6) = 87

45 + 42 = 87

87 = 87

Step 5: Write a sentence to describe your answer: The cost of a pizza is $15, and the cost of a sandwich is $6.

Watch this video to try a few more.

Writing and Solving Systems of Equations Practice

Try these problems to see if you've got it:

1. There are 812 students in school. There are 36 more girls than boys. How many girls and boys are there?

2. Lisa and Beverly have $5 to spend on an afternoon snack at Bob's Burger Joint.   They can buy 2 hamburgers and one soda with no change back. Or they can buy 1 hamburger and 2 sodas and get 40 cents back. How much does a soda cost?

3. Jane has 25 coins in your purse, they are all quarters and dimes. The total amount of money is $5.35. How many quarters and dimes does Jane have?

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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