The system of equations are
,
and
.
Solve the system of equations by elimination method.
\Step 1:
\Eliminate one variable by using two pairs of equations.
\
Subtract the 2nd and 3rd equations to eliminate the one variable.
\
Step 2:
\Solve the system of two equations containing
and
to find
value.
(Divide each side by
)
(Cancel common terms)
Substitute
into system of equation of
and
find
value.
(Substitute
)
(Multiply)
(Subtract
from each side)
(Apply additive inverse property:
)
(Divide each side by
)
(Cancel common terms)
Step 3:
\Substitute values of
and
into one of the original equation to find
value.
(Second equation)
(Substitute
and
)
(Multiply)
(Combine like terms)
(Subtract
from each side)
(Apply additive inverse property:
)
(Divide each side by
)
(Cancel common terms)
Therefore, the solution is
,
and
.
Check solutions for
and
values.
(Third equation)
(Substitute
,
and
)
(Multiply)
(Subtract:
)
The solution of the system is
.
The solution of the system is
.