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# Solving First Degree Equations with Two Unknowns

## Online calculator and solbing procedure for two equations with two unknowns.

First degree equations with two unknowns can be expressed as

a1 x + b1 y = c1                                 (1)

a2 x + b2 y = c2                                 (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.

x + y =

x + y =

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## Citation

• The Engineering ToolBox (2012). Solving First Degree Equations with Two Unknowns. [online] Available at: https://www.engineeringtoolbox.com/equations-two-unknowns-d_1847.html [Accessed Day Month Year].

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9.19.12