Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

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# Solving First Degree Equations with Two Unknowns

First degree equations with two unknowns can be expressed as

a 1 x + b 1 y = c 1 (1)

a 2 x + b 2 y = c 2 (2)

### Example - Two Equations with Two Unknowns

The two equations

3 x + 5 y = 7

4 x - 3 y = 19 <

with the two unknown x and y can be solved by rearranging (1) to

y = (7 - 3 x) / 5

and substituting this expression for y in (2)

4 x - 3 ((7 - 3 x) / 5 ) = 19

- the value for x can then be calculated to

x = 4

By substituting this value for x in expression 1

3 4 + 5 y = 7

- the value for y can be calculated to

y = -1

### Online Calculator for Two Equations with Two Unknowns

The calculator below can be used to estimate x and y values for two equations with two unknowns.

+ =

+ =

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Algebraic Expressions

Principal algebraic expressions formulas.

### Circles within a Rectangle - Calculator

Calculate the maximum number of circles within a rectangle - can be used to calculate the numbers of pipes or wires in a conduit or similar.

### Discrete Data Sets and their Mean, Median and Mode Values

Calculate the arithmetic mean, median and modal values from discrete data sets.

### Numbers - Square, Cube, Square Root and Cubic Root Calculator

Calculate square, cube, square root and cubic root. Values tabulated for numbers ranging 1 to 100.

### Numbers - Standard Form, Scientific and Engineering Notation

The difference between standard, scientific and engineering number notation.

### Prime Numbers

Prime numbers up to 1000.

### Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.

### Solving Equations of the First Degree with One Unknown

Equations with one unknown.

### Solving Quadratic Equation with One Unknown

How to solve a quadratic equation.

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## SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!