Question

5x+3y= -11 , 2x+4y= -10

Answer 1

Required Answer:-

Given:

• 5x + 3y = -11.
• 2x + 4y = -10.

To Find:

• The values of x and y.

Solution:

Given that,

→ 5x + 3y = -11 — (i)

→ 2x + 4y = -10

→ 2(x + 2y) = -10

→ x + 2y = -5

→ x = -2y - 5

Substituting the value of x in (i), we get,

→ 5(-2y - 5) + 3y = -11

→ -10y - 25 + 3y = -11

→ -7y = -11 + 25

→ -7y = 14

→ y = 14/-7

→ y = -2

Putting the value of y, we get,

→ x = -2 × (-2) - 5

→ x = 4 - 5

→ x = -1

Therefore,

$\sf \leadsto\left \{ \large{{x = -1} \atop {y = -2}} \right.$

Answer:

• x = -1 and y = -2.

Answer 2

Required Answer

Give Data:

• 5x+3y= -11 ---- e.q1
• 2x+4y= -10 --- e.q2

To find:

• The values of x and y = ?

Solution:

By multiplying e.q1 with 2.

5x+3y= -11

2(5x+3y= -11)

10x + 6y = -22 ---- e.q3

By multiply e.q2 with 5.

2x+4y= -10

5(2x+4y= -10)

10x + 20y = - 50 ----- e.q4

Now,By subtracting e.q3 and e.q4.

$\mathcal{ \cancel{10x} + 20y = - 50} \\ \mathcal{ \underline{ \cancel{10x} + 6y = -22}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: 14y \: = - 28 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{ \cancel{{ - 28}}} { \cancel{14}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = - 2$

Now put value of y in e.q2.

$\mathcal{ \: \: \: \: \: \: \: 2x+4y= -10} \\ \mathcal{2x + 4( -2) = - 10} \\ \mathcal{ \: \: \: \: \: \: \: \: \: \: 2x - 8 = - 10} \\ \mathcal{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x = - 10 + 8} \\ \mathcal{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x = - 2} \\ \mathcal{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{ - 2}{2} } \\ \mathcal{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 1}$

So the values are

X = -1

Y = -2