Question

8a + 20b = 4
9a + 18b = 3
Solve this equation by substitution method

Answer 1

Answer:

The correct answers are-

1. $a = \frac{ - 1}{3}$
2. $b = \frac{1}{3}$

Step-by-step explanation:

Given,

8a + 20b = 4 (i)

9a + 18b = 3 (ii)

Using equation (i), we get

8a + 20b = 4

8a = 4 - 20b

$•°• \: \: \: a \: = \frac{4 - 20b}{8}$

Substituting the value of a in equation (ii),

9a + 18b = 3

$9 (\frac{4 - 20b}{8}) + 18b = 3$

$\frac{36 - 180b}{8} + 18b = 3$

$\frac{36 - 180b + 144b}{8} = 3$

$36 - 36b = 3 \times 8$

$- 36b = 24 - 36$

$- 36b =- 12$

$b = \frac{ - 12}{ - 36}$

$•°•b = \frac{1}{3}$

Substituting the value of b in equation (i),

8a + 20b = 4

$8a + 20( \frac{1}{3} ) = 4$

$8a = 4 - \frac{20}{3}$

$8a = \frac{12 - 20}{3}$

$8a = \frac{ - 8}{3}$

$a = \frac{ - 8}{3} \times \frac{1}{8}$

$•°•a = \frac{ - 1}{3}$

Adiós! Hope this helps you.