WOLFRAM|DEMONSTRATIONS PROJECT

Solution of Two Equations in Two Unknowns

​
a x + b y = c
a
2
b
3
c
5
d x + e y = f
d
3
e
4
f
2
reset
Consider the system of equations:
2x + 3y = 5
3x + 4y = 2
To solve this system, we use determinants:
x =
Δ
x
Δ
,
y =
Δ
y
Δ
where:
Δ = ae-bd = -1
Δ
x
= ce-bf = 14
Δ
y
= af-cd = -11
The system of equations has a unique solution.
The two straight lines intersect in the point:
( -14 , 11 )
​
​
​
​
​
This Demonstration solves two equations in two unknowns using determinants.