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4x + y = 14. 5x +2y = 19 solve the simultaneous equation

Sagot :

Answer:

(3, 2 )

Step-by-step explanation:

Given the 2 equations

4x + y = 14 → (1)

5x + 2y = 19 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the y- term

- 8x - 2y = - 28 → (3)

Add (2) and (3) term by term to eliminate y

- 3x + 0 = - 9

- 3x = - 9 ( divide both sides by - 3 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

4(3) + y = 14

12 + y = 14 ( subtract 12 from both sides )

y = 2

solution is (3, 2 )

TheAnimeGirl

Step-by-step explanation:

[tex] \underline{ \underline{ \text{USING \: ELIMINATION \: METHOD}}}[/tex]

[tex] \underline{ \underline{ \text{ Solution}}} : [/tex]

  • [tex] \text{4x + y = 14 - - - - - (i)}[/tex]
  • [tex] \text{5x + 2y = 19 \: - - - - - (ii)}[/tex]

Multiply equation ( i ) by 2 & Subtract from ( ii ). The equation ( i ) now becomes 8x +2y = 28 { 2 ( 4x + y ) = 2 × 14 }. Remember that while subtracting the sign of each term of equation ( i ) changes and now , it becomes -8x-2y = -28.

[tex] \text{5x + 2y = 19}[/tex]

[tex] \text{ - 8x - 2y = - 28}[/tex]

_____________________

[tex] \text{ - 3x = - 9}[/tex]

Solve for x :

⤑ [tex] \tt{x = \frac{ - 9}{ - 3}} [/tex]

⤑ [tex] \tt{x = 3}[/tex]

Now , substitute the value of x in equation ( ii ) :

⟼ [tex] \text{5 × \: 3 + 2y = 19}[/tex]

⟼ [tex] \text{15 + 2y = 19} [/tex]

⟼ [tex] \text{2y = 19 - 15}[/tex]

⟼ [tex] \text{2y = 4}[/tex]

⟼ [tex] \text{y = 2}[/tex]

[tex] \pink{ \boxed{ \boxed{ \tt{⤿ \: Our \: final \: answer : \boxed{ \boxed{ \tt{x = 3 \: and \: y = 4}}}}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day night ! ♡

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