Question

(3) 3x - 2y =5/2 ; 1/3x + 3y = -4/3​

Answer 1

Answer:x=2/5 & y=-13/20

Step-by-step explanation:

3x-2y=5/2.......(1)

1/(3x+3y)=-4/3......(2)

From (1),

6x-4y-5=0......(3)

From (2),

3=-4(3x+3y)

Or,3=-12x-12y

Or,12x+12y+3=0......(4)

Multiply (3) by 2 on both sides we get

12x-8y-10=0.....(5)

Subtractibg (5) from (4) we gey

20y+13 =0

Therefore y=(-13/20)

Now, 6x=4y+5

6x=4(-13/20)+5

Or,6x=(-13+25)/5

Or,6x=12/5

Therefore x=2/5

Answer 2

Answer:

$x=\frac{1}{2} \: and \: y = \frac{-1}{2}$ is the solution of the given simultaneous equations.

Step-by-step-explanation:

The given linear equations are

${3x - 2y = \frac{5}{2}}$ and ${\frac{1}{3}x + 3y = \frac{-4}{3}}$

Let's find the solution of the given linear equations by Cramer's rule as by other methods, it will be difficult to find the solutions.

${3x - 2y = \frac{5}{2}}$

Here, ${a}_{1}=3,{b}_{1}=-2{c}_{1}=\frac{5}{2}$

${\frac{1}{3}x + 3y = \frac{-4}{3}}$

${a}_{2}=\frac{1}{3},{b}_{2}=3,{c}_{2}=\frac{-4}{3}$

$D=\left|[\begin{array}{c c }{a}_{1}& {b_{1}\\{a}_{2}&{b} _{2}\end{array\right]|=\left|[\begin{array{c c}3&-2\\\frac{1}{3}&3\end{array} \right]|={3}\times{3}-(-2)\times\frac{1}{3}=9+\frac{2}{3}=\frac{27+2}{3}=\frac{29}{3}\\{D}_{x}=\left|[\begin{array}{c c }{c}_{1}& {b}_{1} \\{c}_{2}&{b}_{2}\end{array} \right]|=\left|[\begin{array{c c}\frac{5}{2}&-2\\\frac{-4}{3}&3\end{array}\right]|\\=\frac{5}{2}\times3-(-2)\times\frac({-4}{3})\\=\frac{15}{2}-\frac{8}{3}=\frac{45-16}{6}=\frac{29}{6}\\{D}_{y}=\left|[</p><p>\begin{array}{c c }{a}_{1}& {c}_{1} \\</p><p>{a}_{2}&{c}_{2}\end{array}\right]|=\left|[\begin{array{c c}\3&\frac{5}{2}\\\frac{1}{3}&\frac{-4}{3}\end{array}\right]|=3\times\frac({-4}{3})-\frac{5}{2}\times\frac{1}{3}=-4-\frac{5}{6} =\frac{-24-5}{6}=\frac{-29}{6}$

By Cramer's rule,

$x=\frac{D}_{x{D}} =\frac{\frac{29}{6}{29}{3}=\frac{29}{6}\times\frac{3}{29}=\frac{1}{2}$

$y=\frac{D}_{y{D}} =\frac{\frac{-29}{6}{29}{3}=\frac{-29}{6}\times\frac{3}{29}=\frac{-1}{2}$

Ans.:

$x=\frac{1}{2} \: and \: y = \frac{-1}{2}$ is the solution of the given simultaneous equations.