Question

6x-7y=16,9x-5y=35(Cramer's rule)

Answer 1

Answer:

$\Large\boxed{X=5 \quad Y=2}$

Step-by-step explanation:

$\Large\boxed{\textnormal{SUBJECT: MATH}}}$

$\Large\boxed{\textnormal{LESSON: HOW TO SOLVE WITH CRAMER'S RULES!}}}$

GIVEN:

6x-7y=16 & 9x-5y=35 (by using with Cramer's rule.)

To solve this problem, first you have to use Cramer's rule formula from left to right numbers.

Isolate by the x and y from one side of the equation.

SOLUTIONS:

First, you have to use Cramer's rule formula.

$\Large\boxed{\textnormal{CRAMER'S RULES FORMULA}}}$

$\displaystyle \frac{D_X}{D},\quad Y=\frac{D_Y}{D},\quad Z=\frac{D_Z}{D}$

$\displaystyle \begin{bmatrix}6x-7y=16\\ 9x-5y=35\end{bmatrix}$

Use matrix of coefficients.

$\displaystyle m=\begin{pmatrix}6&-7\\ 9&-5\end{pmatrix}$

Solve.

$\displaystyle \begin{pmatrix}16\\ 35\end{pmatrix}$

Try to replace by the x value of the number.

$\displaystyle M_X=\begin{pmatrix}16&-7\\ 35&-5\end{pmatrix}$

Replace by the y value of the number.

$\displaystyle M_Y=\begin{pmatrix}6&16\\ 9&35\end{pmatrix}$

$\dispalystyle m=\begin{pmatrix}6&-7\\ 9&-5\end{pmatrix}$

Used matrix formula.

$\displaystyle \det \begin{pmatrix}A\:&\:B\:\\ C\:&\:D\:\end{pmatrix}\:=\:AD-BC$

$\displaystyle 6(-5)-(-7)*9$

PEMDAS stands for (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract) numbers from left to right. Please Excuse My Dear Aunt Sally!

BOMDAS stands for (Brackets, Of, Multiply, Divide, Add, and Subtract) the numbers from left to right.

Solve with order of operations.

$\displaystyle -6*5+7*9$

Multiply.

$\displaystyle 6*5=30$

$\displaystyle -30+7*9$

$\displaystyle 7*9=63$

Rewrite the whole problem down.

$\displaystyle -30+63$

Add & subtract the numbers from left to right.

$\displaystyle -30+63=33$

$\displaystyle D=33$

$\displaystyle D_X=165$

$\displaystyle D_Y=66$

D it denotes by the determinant.

$\displaystyle X=\frac{D_X}{D}=\frac{165}{33}$

Solve.

Divide.

$\displaystyle 165\div33=\boxed{5}$

$\Large\boxed{X=5}$

$\displaystyle Y=\frac{D_Y}{D}=\frac{66}{33}$

Solve. (Simplify/ to find the answer.)

Divide the numbers from left to right.

$\displaystyle 66\div33=\boxed{2}$

$\Large\boxed{Y=2}$

$\Large\boxed{X=5, \quad Y=2}$

In conclusion, the correct answer is x=5 and y=2.