Question

X-2/3y=8/3 , 2x/5-y=7/5 by elimination method

Answer 1

Answer:

$\large\bold\red{x = \frac{78}{33}}\\\\\large\bold\red{y = - \frac{5}{11} }$

Step-by-step explanation:

Given,

Two linear equations such that,

$x - \frac{2}{3} y = \frac{8}{3} \: \: .............(1)$

And,

$\frac{2}{5} x - y = \frac{7}{5} \: \: \: \: ..........(2)$

Now,

To solve this pair of linear equations,

Multiply the eqn (1) by $\frac{2}{5}$

Therefore,

We get,

$= > \frac{2}{5} x - \frac{4}{15} y = \frac{16}{15} \: \: \: \: \: ........(3)$

Now,

Eliminating the x term,

Subtract eqn (3) from eqn (2)

Therefore,

We get,

$= > - y - ( - \frac{4}{15} y) = \frac{7}{5} - \frac{16}{15} \\ \\ = > - y + \frac{4}{15} y = \frac{(7 \times 3) - 16}{15} \\ \\ = > \frac{ - 15y + 4y}{ \cancel{15}} = \frac{21 - 16}{ \cancel{15}} \\ \\ = > - 15y + 4y = 21 - 16 \\ \\ = > - 11y = 5 \\ \\ = > \large \boxed{ \bold{y = - \frac{5}{11} }}$

Now,

Putting this value in eqn (2),

We get,

$= > x - \frac{2}{3} \times ( - \frac{ 5}{11} ) = \frac{8}{3} \\ \\ = > x + \frac{10}{33} = \frac{8}{3} \\ \\ = > x = \frac{8}{3} - \frac{10}{33} \\ \\ = > x = \frac{(8 \times 11) - 10}{33} \\ \\ = > x = \frac{88 - 10}{33} \\ \\ = > \large \boxed{ \bold{x = \frac{78}{33}}}$

Answer 2

Question :----

• x -(2y/3) = 8/3
• 2x/5 - y = 7/5
• Solve both by elimination method ?

solution :----

we have to make any term same first my multiply or divide , and than we will subtract the equation ..

Let ,,

x -(2y/3) = 8/3 ------------------ Equation (1)

2x/5 - y = 7/5 ------------------ Equation (2)

now , Lets multiply Equation (1) by 2/5 so, that, x will be same ,,, and than we will subtract Equation (2) from Equation (1) we get,,,

2/5(x- 2y/3) = 2/5 × 8/3

→ 2x/5 - 4y/15 = 16/15 ------------------ Equation (3)

Now, subtracting Equation (2) from Equation (3) we get,

[2x/5 - 4y/15] - [2x/5 - y] = 16/15 - 7/5

→ 2x/5 - 2x/5 - 4y/15 + y = 16/15 - 7/5

→. (-4y+15y) /15 = (16-21) /15

→ 11y/15 = -5/15

15 cancel in denominator both sides,

→ 11y = -5

→ y = -5/11 (Ans)

Now, putting value of y in any Equation we get,,,

→ x - 2y/3 = 8/3

→ x - 2/3×(-5/11) = 8/3

→ x + 10/33 = 8/3

→ x = 8/3 - 10/33

→ x = 88 -10/33

→ x = 78/33 ...

so, value of x is 78/33 and y is (-5/11)

(Hope it Helps you)