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Simultaneous Equations for Circuit Analysis
25 questions By Tony R. Kuphaldt
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Question 1 of 25
Solve this equation for the value of x:
x + 5 = 8 How many exact solutions does the above equation have?
Now, determine a few different solutions for the following equation:
x + y = 8 How many exact solutions does this equation have? Plot this equation’s solutions on the following graph:
Reveal answerIf x + 5 = 8 , then x = 3 (exactly one solution) If x + y = 8 , then there are an infinite number of solutions: 
Follow-up question: find the solution to x + 5 = 8 on this same graph.
Notes:This question begins with an extremely simple equation having one solution and moves on to another simple equation having an infinite number of solutions. While an infinitude of correct answers may seem impossible to rationally deal with, a graph handles it quite nicely, the multitude of correct answer pairs represented as a line on a graph with infinite length.
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Question 2 of 25
Plot the solutions to the equation y + x = 8 on a graph:
On the same graph, plot the solutions to the equation y − x = 3. What is the significance of the point where the two lines cross?
Reveal answer
The point of intersection between the two lines represents the one solution set that satisfies both equations (where x = 2.5 and y = 5.5).
Notes:The purpose of this question is to gently introduce students to the concept of simultaneous systems of equations, where a set of solutions satisfies more than one equation at a time. It is important for students to understand the basic concepts of graphing before they try to answer this question, though.
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Question 3 of 25
What does it actually mean to obtain a solution for a “simultaneous” system of equations? For example, if 2x + y = 7 and x − y = −1, what do the solution values (x = 2 ; y = 3) represent?
If we were to graph both these linear equations on a Cartesian (x, y) coordinate system, where would the solution (2,3) be located on the graph?
Reveal answerThe solutions for a system of equations represent a unique combination of values that satisfy all equations in that system. For a two variable system, the solution is the intersection of two lines.
Notes:Many students have difficulty grasping the significance of systems of equations. Discuss the meaning of equations, and systems of equations, with your students, making sure that the concept of simultaneity (solutions satisfying all equations at once) is made clear.
