Question

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

Answer 1

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,

`\implies \: \displaystyle\sf{x \: = \: 6 - y}`

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

`\implies \: \displaystyle\sf{2 \: (6 - y) \: = \:15 }`

`\implies \: \displaystyle\sf{2 \: * (6 - y) \: = \:15 }`

`\implies \: \displaystyle\sf{12 - 2y \: = \:15 }`

Transposing 12 to R.H.S.,

`\implies \: \displaystyle\sf{ - 2y \: = \:15 - 12 }`

`\implies \: \displaystyle\sf{ - 2y \: = \:3}`

`\implies \: \displaystyle\bf{ y \: = \: - (3)/(2) }`

Therefore, value of y is - 3/2.

★ Finding out value of x:-

`\implies \: \displaystyle\sf{x \: = \: 6 - y }`

`\implies \: \displaystyle\sf{x \: = \: 6 - ( ( - 3)/( 2) )}`

`\implies \: \displaystyle\sf{x \: = \: (12 + 3)/(2) }`

`\implies \: \displaystyle\bf{x \: = \: (15)/(2) }`

Henceforth,

• Value of x is 15/2.