The equation is .
The matrices have the same dimensions and the corresponding elements are equal. Form the two linear equations by writing the sentences to show the equality.
\ Equation(1)
Equation(2)
Solve the system using substitution method.
\The first equation is .
Apply subtraction property of equality: If , then
.
(Subtract x from each side)
Apply commutative property of addition: a + b = b + a.
\ (Apply Additive inverse property:
)
(Divide each side by 3)
(Cancel common terms)
Substitute in second equation.
Apply multiplication property of equality: if , then
.
(Multiply each side by 3)
(Cancel common terms)
(Multiply:
)
(Subtract:
)
Apply addition property of equality: if , then
.
(Add 13 to each side)
(Apply Additive inverse property:
13 + 13 = 0)
(Add:
)
Apply division property of equality; if , then
.
(Divide each side by 8)
(Divide:
)
Substitute in first equation.
According to subtraction property of equality: if , then
.
(Subtract 2 from each side)
Apply commutative property of addition: a + b = b + a.
\ (Apply Additve inverse property: 2
2 = 0)
(Add:
)
(Divide each side by 3)
(Simplify)
The solution is .