# 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.

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