Elimination method:
\Given equations are,
\ ----------(1)
----------(2)
When the coefficients of a variable and
are same,
subtracting the equations will eliminate the variable.
Subtracting (2) and (1) equations will eliminate the variable y.
\ (Subtracting (2) and (1) equations)
Apply division property of equality: If a = b then .
(Divide each side by 4)
(Cancel common terms)
Substitute for x in either equation to find y.
(First equation)
(Substitute
)
(Apply multiplicative identity property:
)
Apply commutative property of addition: .
(Subtract 6 from each side)
(Apply additive inverse property:
)
(Apply additive identity property:
)
(Subtract:
)
(Multiply each side by negative sign)
(Product of two same signs is positive sign)
(Divide each side by 2)
(Cancel common terms)
(Divide:
)
Check the solution:
\To Check, substitute and
in either equation.
(First equation)
(Substitute
and
)
(Multiply:
)
(Subtract:
)
The solution is true.
The solution is .