a system of equations

USAGE SUMMARY

The phrase "a system of equations" is correct and usable in written English.
It can be used in mathematical contexts to refer to a set of equations that are considered together, often to find common solutions. Example: "To solve the problem, we need to set up a system of equations that represents the relationships between the variables."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Commodity input coefficients are postulated and for each industry the implied input demand vector is equated with the observed use vector; a system of equations must be solved.

Journal of Economic Structures

He showed that the desired result is obtainable by the straightforward solution of a system of equations involving the costs of the materials at their sources and the costs of shipping them by alternative routes.

Encyclopedia Britannica

Try to describe that set-up using a system of equations that could be solved using a computer.

Science Magazine

Finally, a system of equations is solved by using a numerical simulation to justify our results.

Advances in Difference Equations

A VAR is a system of equations which is rooted in the Box-Jenkins procedure.

Agricultural and Food Economics

A system of hypotheses can be modeled as a system of equations [27].

Journal of Internet Services and Applications

In this method, using operational matrices, the integral equation turns into a system of equations.

Mathematical Sciences

A system of equations representing the model was simultaneously solved using the implicit finite difference method.

Renewable Energy

The solution reduces to a system of equations relating to the generalized reactions at supports.

Journal of Sound and Vibration

A system of equations can be expressed elegantly using a coefficient matrix and column vectors.

Numerical Linear Algebra with Applications Using MATLAB

The presented model of exchange sorption is a system of equations, solved numerically.

Fuel Processing Technology

Expert writing Tips

Best practice

When describing a complex phenomenon, clarify which variables are represented by which equations within the "a system of equations" to enhance readability and understanding.

Common error

Avoid assuming that solving "a system of equations" implies a causal relationship between the variables; it merely describes a mathematical relationship, which needs separate validation.

Linguistic Context

The phrase "a system of equations" functions as a noun phrase, typically serving as the subject or object of a sentence. It refers to a collection of mathematical equations that are considered together for a common solution. Ludwig AI confirms its broad applicability across various scientific and mathematical contexts.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "a system of equations" is a noun phrase widely used in formal and scientific contexts to describe a set of mathematical equations solved together. As indicated by Ludwig AI, the phrase is grammatically correct and particularly prevalent in scientific literature. While alternative phrases like "simultaneous equations" or "set of equations" exist, "a system of equations" accurately and effectively conveys the concept of interrelated mathematical expressions. It's important to clarify variables and relationships to avoid misinterpretations and enhance clarity in writing. The phrase's high frequency and consistent usage in authoritative scientific sources reinforce its reliability and precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

simultaneous equations

This alternative emphasizes the concept of equations that are solved together.

equation system

A more concise way of expressing the same concept, inverting the order of words.

set of equations

This is a more general term referring to a collection of equations.

mathematical model

This broadens the concept to include the entire model, of which the equations are a part.

equation model

More concise form that focuses on the relationship.

system of formulas

Utilizes the synonym "formulas" to replace "equations", slightly shifting the context.

mathematical representation

This is a more abstract way to refer to the equations as a form of representing a problem.

model equations

Focuses on equations used in mathematical modeling.

formulaic system

Emphasizes the structured arrangement of formulas.

quantitative model

Highlights the model's ability to provide quantifiable results.

FAQs

How can "a system of equations" be used in a sentence?

You can use "a system of equations" to describe a set of equations that are solved together, such as, "We used "simultaneous equations" to find the solution."

What is the difference between "a system of equations" and "a set of equations"?

While both phrases refer to multiple equations, "a system of equations" often implies that the equations are related and solved together, whereas "a set of equations" may simply refer to a collection of unrelated equations.

When is it appropriate to use "a system of equations" instead of a simpler equation?

"A system of equations" is appropriate when you need to model multiple interconnected relationships. A single equation is sufficient for isolated relationships.

What are some real-world examples where "a system of equations" is used?

"A system of equations" is used in physics to model motion, in economics to model supply and demand, and in computer graphics to render images.