Question

3x-5y-4=0 and 9x=2y+7
Solve by elimination method
And substitution method

Answer 1

$\sf Elimination \ Method$

Given

3x - 5y - 4 = 0

→ 3x - 5y = 4..............( i )

And, 9x = 2y + 7

→ 9x - 2y = 7.................( ii )

Now, by multiplying with 3 on both sides in first equation, we get

3(3x - 5y) = 3(4)

→ 9x - 15y = 12............ (iii)

Now, Subtract equation (ii) from equation (iii)

→ 9x - 15y - (9x - 2y) = 12 - 7

→ 9x - 15y - 9x + 2y = 5

→ -13y = 5

→ y = -5/13

Substitute the value of y to get the value of x.

9x = 2y + 7

→ 9x = -10/13 + 7

(as, y = -5/13, → 2y = -10/13)

→ 9x = (-10 + 91)/13

(after taking LCM ↑)

→ 9x = 81/13

→ x = 9/13

$\sf Substitution \ Method$

Given 9x = 2y + 7

→ x = (2y + 7)/9

And, 3x - 5y - 4 = 0

So, substitute the value of x in terms of y in second equation

→ 3(2y + 7)/9 - 5y - 4 = 0

→ (2y + 7)/3 - 5y - 4 = 0

(cancelling 9 in the denominator by 3)

→ (2y + 7 - 15y)/3 - 4 = 0

(by taking LCM)

→ (7 - 13y)/3 = 4

→ 7 - 13y = 3(4)

→ 7 - 13y = 12

→ - 13y = 5

→ y = -5/13

Again, by putting the value of y, we will get the value of x.

Hence,

$\huge\mathfrak{Answer}$

$\huge{x = \frac{9}{13}}$

$\huge{y = \frac{-5}{13}}$