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2x + 3y = 15
x + y = 6
work out x and y

Sagot :

Answer:

x=3

y=3

Step-by-step explanation

ItzStarzMe

Solution :

Here we have been given with two equations and we will solve them by substitution by elimination method.

  • 2x + 3y = 15 (Equation No 1)
  • x + y = 6 (Equation No 2)

Transposing y in 1st equation from L.H.S. to R.H.S. it would be negative,

[tex] \implies \: \displaystyle\sf{x \: = \: 6 - y}[/tex]

Now, we would substitute this value of x in Equation No 1.

[tex] \implies \: \displaystyle\sf{2 \: (6 - y) \: = \:15 }[/tex]

[tex] \implies \: \displaystyle\sf{2 \: \times (6 - y) \: = \:15 }[/tex]

[tex]\implies \: \displaystyle\sf{12 - 2y \: = \:15 }[/tex]

Transposing 12 to R.H.S.,

[tex] \implies \: \displaystyle\sf{ - 2y \: = \:15 - 12 }[/tex]

[tex]\implies \: \displaystyle\sf{ - 2y \: = \:3}[/tex]

[tex]\implies \: \displaystyle\bf{ y \: = \: - \dfrac{3}{2} }[/tex]

Therefore, value of y is - 3/2.

★ Finding out value of x:-

[tex] \implies \: \displaystyle\sf{x \: = \: 6 - y }[/tex]

[tex]\implies \: \displaystyle\sf{x \: = \: 6 - ( \dfrac{ - 3}{ 2} )}[/tex]

[tex]\implies \: \displaystyle\sf{x \: = \: \frac{12 + 3}{2} }[/tex]

[tex]\implies \: \displaystyle\bf{x \: = \: \frac{15}{2} }[/tex]

Henceforth,

  • Value of x is 15/2.

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