Solve the pair of simultaneous equations

7x - 4y=21       multiply both sides by  5                                    35x - 20y  = 105         (1)

3x = 5y+4   rearrange as   3x - 5y  =  4    multiply both sides by -4        -12x +20y  =  -16        (2)

Add  (1)  and (2)

23x  = 89      divide both sides by 23

x = 89/23      and using (1) to find y, we have

35(89/23) - 20 y = 105

20y = 35(89/23) -105  

4y = 7(89/23) - 21

y = [7(89/23) - 21] / 4   =  35/23

Solve the following system:
{7 x-4 = 21 |     (equation 1)
3 x = 5 y+4 |     (equation 2)
Express the system in standard form:
{7 x+0 y = 25 |     (equation 1)
3 x-5 y = 4 |     (equation 2)
Subtract 3/7 × (equation 1) from equation 2:
{7 x+0 y = 25 |     (equation 1)
0 x-5 y = (-47)/7 |     (equation 2)
Multiply equation 2 by -7:
{7 x+0 y = 25 |     (equation 1)
0 x+35 y = 47 |     (equation 2)
Divide equation 2 by 35:
{7 x+0 y = 25 |     (equation 1)
0 x+y = 47/35 |     (equation 2)
Divide equation 1 by 7:
{x+0 y = 25/7 |     (equation 1)
0 x+y = 47/35 |     (equation 2)
Collect results:
Answer: | 
| {x = 25/7
y = 47/35