Systems of Equations (Word Problems)

A. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

B. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

C. Solve real-world and mathematical problems leading to two linear equations in two variables.
For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Common Core: 8.EE.8c

Suggested Learning Targets

• I can identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection of their graphs.
• I can describe the point(s) of intersection between two lines as the points that satisfy both equations simultaneously.
• I can define “inspection.”
• I can solve a system of two equations (linear) in two unknowns algebraically.
• I can identify cases in which a system of two equations in two unknowns has no solution.
• I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions.
• I can solve simple cases of systems of two linear equations in two variables by inspection.
• I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations.
• I can represent real-world and mathematical problems leading to two linear equations in two variables.

Systems of equations word problem (coins)

Example:
A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters does he have?

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Word problem using system of equations (investment-interest)

Example:
A woman invests a total of $20,000 in two accounts, one paying 5% and another paying 8% simple interest per year. Her annual interest is $1,180. How much did she invest in each rate?

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Systems of Equations Word Problems

Example:
The sum of two numbers is 16. One number is 4 less than 3 times the other. Find the numbers.

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Systems of Equations (word problems)

Example:
Two times a number plus ten times a second number is twenty. Thirty times the second number plus three times the first number is 45. What are the two numbers?

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Systems of Equations-Word Problems

How to solve a word problem involving a system of 2 equations with 2 variables?

Example:
Three coffees and two muffins cost a total of 7 dollars. Two coffees and four muffins cost a total of 8 dollars. What is the individual price for a single coffee and a single muffin?

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How to translate words or word problems into a systems of equations?

Example:
A coin collection is made up of 34 coins comprised of nickels and dimes. The total value of the collection is $1.90. How many dimes and nickels made up this collections?

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Systems of Equations - word problems
Examples of setting up word (or application) problems solved by a system of equations.

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Example:
For some reason, in our math class, there are 14 more boys than there are girls. If a total of 32 students are in the class, how many boys and how many girls are there?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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