Question

» x - 2/3y = 8/3

» 2x/5 - y = 7/5

Find out x and y .
​

Answer 1

Answer:

Sum of first n terms of an arithmetic sequence is 3n

2

+n.

Let a

1

denotes first term of the sequence,

a

2

denotes second term of the sequence,

d denotes common difference of the sequence,

S

n

denotes sum of first n terms of the sequence.

S

n

=3n

2

+n

S

1

=a

1

=3(1)

2

+1=4

S

2

=a

1

+a

2

=3(2)

2

+2=14

∴a

1

+a

2

=14

∴a

1

+a

1

+d=14

∴2a

1

+d=14

∴2(4)+d=14

∴d=6

First term of the sequence is 4 and common difference is 6.

Step-by-step explanation:

hope you understand

Answer 2

Step-by-step explanation:

$x - \frac{2}{3} y = \frac{8}{3} \\ multiplying \: with \: 3 \: throughout \\ 3x - 2y = 8 \: \: \: \: \: \: \: eqn(1)$

$\frac{2}{5} x - y = \frac{7}{5} \\ multiplying \: by5 \\ 2x - 5y = 7 \: \: \: \: \: \: \: \: eqn(2)$

$eqn(1) \times 2 - eqn(2) \times 3 \: gives$

$- 4y + 15y = 16 - 21$

$11y = - 5 \\ y = \frac{ - 5}{11}$

using this in eqn (1) gives

$3x - 2y = 8 \\ 3x + \frac{10}{11} = 8 \\ 3x = 8 - \frac{10}{11} \\ 3x = \frac{78}{11} \\ x = \frac{26}{11}$