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Manny is making 12 quarts of orange juice from concentrate and water. The number of quarts of water is 3 times the number of quarts of concentrate. How many quarts of concentrate and how many quarts of water does Manny need?
Manny needs 3 quarts juice concentrate and 9 quarts water.
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Alisha is making an 18 ounce coffee beverage that is made from brewed coffee and milk. The number of ounces of brewed coffee is 5 times greater than the number of ounces of milk. How many ounces of coffee and how many ounces of milk does Alisha need?
Alisha needs 15 ounces of coffee and 3 ounces of milk.
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Key concepts
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To solve a system of linear equations by graphing
- Graph the first equation.
- Graph the second equation on the same rectangular coordinate system.
- Determine whether the lines intersect, are parallel, or are the same line.
- Identify the solution to the system.
If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.
If the lines are parallel, the system has no solution.
If the lines are the same, the system has an infinite number of solutions.
- Check the solution in both equations.
- Determine the number of solutions from the graph of a linear system
- Determine the number of solutions of a linear system by looking at the slopes and intercepts
- Determine the number of solutions and how to classify a system of equations
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Problem Solving Strategy for Systems of Linear Equations
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Read the problem. Make sure all the words and ideas are understood.
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Identify what we are looking for.
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Name what we are looking for. Choose variables to represent those quantities.
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Translate into a system of equations.
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Solve the system of equations using good algebra techniques.
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Check the answer in the problem and make sure it makes sense.
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Answer the question with a complete sentence.
Practice makes perfect
Determine Whether an Ordered Pair is a Solution of a System of Equations . In the following exercises, determine if the following points are solutions to the given system of equations.
Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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