Question

How do you solve 4x+y=−9 and 3x+7y=37?

Answer 1

Given equations,

4x + y = - 9 ...... (i)

3x + 7y = 37 ..... (ii)

By using Elimination method,

Multiplying equation (i) by 7,

7(4x + y = - 9)

28x + 7y = - 63 ..... (iii)

Subtracting equation (iii) from equation (ii),

$28x \: + 7y \: = - 9 \\ 3x \: + \: 7y \: = \: 37$

$28x + \cancel{7y} = - 9 \\ 3x + \cancel{7y} = 37$
By subtracting we obtain,
=> 24x = 28

=> x = $\frac{28}{24}$

=> x = $\frac{\cancel{28}}{\cancel{24}}$

=> x = $\frac{14}{12}$

=> x = $\frac{\cancel{14}}{\cancel{12}}$

=> x = $\frac{7}{6}$

$\fbox{\bold{\mathsf{x = \frac{7}{6}}}}$

Substituting x = $\frac{7}{6}$ in equation (i),

4x + y = - 9

$4(\frac{7}{6}) + y = - 9$

$\cancel{4}(\frac{7}{\cancel{6}} + y = - 9$

$2(\frac{7}{3}) + y = - 9$

$\frac{14}{3} + y = - 9$

$\frac{14 + 3y}{3} = - 9$

$14 + 3y = \frac{- 9}{3}$

$14 + 3y = \frac{\cancel{-9}}{\cancel{3}}$

14 + 3y = - 3

3y = - 3 - 14

3y = - 17

y = $\frac{-17}{3}$

$\fbox{\bold{\mathsf{y = \frac{-17}{3}}}}$

$\fbox{\bold{\mathsf{\large{\therefore x = \frac{7}{6} \& y = \frac{-17}{3}}}}}$

Answer 2

Answer:

x = - 4, y = 7

Step-by-step explanation:

4x + y = - 9...... (i)

3x + 7y = 37.......(ii)

We will solve this question, using elimination and substitution method;

Multiplying eqⁿ (i) by 7, we get ;

4x + y = - 9

⇒ 7 (4x + y) = 7 * (-9)

⇒ 28x + 7y = - 63...... (iii)

Subtracting eqⁿ (ii) from (iii), we get;

$28x + 7y = - 63 \\ \: 3x \: + \: 7y = \: \: \ 37 \\ - \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: -$

________________

$25x = - 100 \\ \\ x = \frac{ - 100}{25} \\ \\ \boxed{ \bf x = - 4}$

Substituting the value of x in (i),

4x + y = - 9

⇒ 4 (-4) + y = - 9

⇒ - 16 + y = - 9

⇒ y = - 9 + 16

$\boxed{\bf \implies y = 7}$

Hence, the value of x is - 4 and y is 7.