WOLFRAM|DEMONSTRATIONS PROJECT

Opposite Coefficients Method for Solving Two Equations in Two Unknowns

​
coefficients of the first equation
4
4
4
4
3
3
coefficients of the second equation
6
6
3
3
2
2
To eliminate x (step 1),
multiply the first equation by g and
the second equation by h,
then add the two equations (step 2).
Automatic elimination:
g
3
h
-2
show steps
1
2
3
Solve the system of the equations:
4x+4y3
6x+3y2
12x+12y9
-12x-6y-4
6y5
y
5
6
4x+
10
3
3
x-
1
12
This Demonstration solves the system of linear equations
ax+by=c
,
dx+ey=f
with the opposite coefficient method.
Step 1: to eliminate
x
, multiply the first equation by
d
and the second by
-a
, and add the equations. Even better: multiply the first with
g=lcm(a,d)/a
and the second with
h=-lcm(a,d)/d
. (Here
lcm(a,d)
means the least common multiple of
a
and
d
.)
Step 2: add equations and solve a new equation for
y
.
Step 3: substitute the solution for
y
into the first given equation, and solve the new equation for
x
.