Solving 4 product equations 4 unknowns

In summary, a 4 product equation with 4 unknowns is a mathematical equation with four variables and four products. The general steps for solving such an equation involve simplifying, factoring, and setting each factor equal to zero. This type of equation can have multiple solutions, and common strategies for solving it include substitution, elimination, and Gaussian elimination. Real-world applications of solving 4 product equations with 4 unknowns can be seen in various fields such as engineering, physics, and economics.
  • #1
golmschenk
36
0
I ran into this in my research and I'm certain it should be extremely simple, but for some reason I can seem to remember how to do it. If I have a setup such as:
a1*b1=c1
a2*b1=c2
a1*b2=c3
a2*b2=c4
And the c's are known values, how do I solve for the a's and b's in terms of c's?
 
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  • #2
Take the first two equations and divide them to eliminate b1

Take the last two and divide them and eliminate b2


You will now have two equations in a1 and a2
 

FAQ: Solving 4 product equations 4 unknowns

What is a 4 product equation with 4 unknowns?

A 4 product equation with 4 unknowns is a mathematical equation with four different variables or unknowns and four different products or terms. It is typically in the form of a polynomial equation, where each term is multiplied together and then added to the other terms.

What are the steps for solving a 4 product equation with 4 unknowns?

The general steps for solving a 4 product equation with 4 unknowns are as follows:
1. Simplify the equation by combining like terms and moving all terms to one side.
2. Factor out any common terms.
3. Use the distributive property to expand any parentheses.
4. Set each factor equal to zero and solve for the unknowns.
5. Check your solutions by plugging them back into the original equation.

Can a 4 product equation with 4 unknowns have multiple solutions?

Yes, a 4 product equation with 4 unknowns can have multiple solutions. This is because there are four unknown variables and only four equations, so there can be more than one combination of values that satisfy all four equations simultaneously.

What are some common strategies for solving a 4 product equation with 4 unknowns?

Some common strategies for solving a 4 product equation with 4 unknowns include using substitution, elimination, or the Gaussian elimination method. These methods involve manipulating the equations in various ways to isolate and solve for the unknown variables.

What are some real-world applications of solving 4 product equations with 4 unknowns?

Solving 4 product equations with 4 unknowns can be useful in fields such as engineering, physics, and economics. These equations can be used to model and solve complex systems with multiple variables, such as electrical circuits, chemical reactions, or supply and demand relationships.

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