# Two Equations and Two Unknowns

## Online calculator for two equations and two unknowns.

Two 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.