Solving First Degree 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.