Question

solve the following linear equations:
2x-y=11 and 5x+4y=1​

Answer 1

Step-by-step explanation:

5(2x-y=11)

2(5x+4y=1)

10x-5y=55

(-)10x+8y=2

-/

-13y=53

y=-53/13

substitute in one of the equation to find x

Answer 2

Answer:

$\blue⇝ \sf{Solution:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue⇝ \sf{5x + 4y = 1 - - - - - - eq(2)}$

$\sf\blue{Multiply \: 5 × eq (3) \: and \: 2 × eq (4) }$

$\blue⇝ \sf{5(2x - y = 11)}$

$\blue⇝ \sf{10x - 5y = 55 - - - - - eq(3)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue⇝ \sf{2(5x + 4y = 1)}$

$\blue⇝ \sf{10x + 8y = 2 - - - - - eq(4)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf\blue{Now \: Use \: Elimination \: Method}$

$\blue⇝ \sf{ \cancel10x - 5y = 55 }$

$\blue⇝ \sf{ \cancel10x + 8y = 2 }$

$\blue⇝ \sf{ \: - \: \: \: \: \: \: \: - \: \: \: \: \: - }$

$\blue⇝ \sf{ -13y = 53}$

$\blue⇝ \sf{ y = \frac{-53}{13} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf\blue{Substitute \: Value \: of \: y \: in \: eq(1) }$

$\blue⇝ \sf{2x - y = 11}$

$\blue⇝ \sf{2x - \frac{(-53)}{13} = 11}$

$\blue⇝ \sf{2x = 11 - \frac{53}{13} }$

$\blue⇝ \sf{2x = \frac{143}{13} - \frac{53}{13} }$

$\blue⇝ \sf{2x = \frac{90}{13} }$

$\blue⇝ \sf{x = \frac{ \cancel90}{13} \times \frac{1}{ \cancel2} }$

$\blue⇝ \sf{x = \frac{ 45}{13} }$