Solve the following systems of equations:

where, x + y ≠ 0 and x – y ≠ 0

Given: the following systems of equations:

...... (1)

...... (2)

To find: The value of x and y.

Explanation:

Take

The equations become:

6u=7v+3

6u–7v=3 ...... (3)

And,

⇒ 3u=2v

3u–2v=0 ...... (4)

To find the value of u and v,

Multiply eq. 4 with 2 and subtract it from eq. 3

⇒ 6u–7v–2(3u–2v) =3–0

⇒ 6u–7v–6u+4v=3

⇒ –3v=3

⇒ v=–1

Put the value of v in eq. 4 to get,

⇒ 3u–2(–1) =0

⇒ 3u+2=0

⇒ 3u=–2

Now,

⇒ 3 = –2(x + y)

⇒ 3=–2x–2y ..... (5)

⇒ x–y=–1 .... (6)

Multiply eq. 6 with 2 and add to eq. 5

⇒ 2(x–y) + (–2x–2y) =–2+3

⇒ –2y–2y–2x–2y=1

⇒ –4y=1

Now put the value of y in eq. 6 to get,

Hence the values are .