math algebra?

Question

Please someone help me with this, the fractions completely push me of track. Thanks.
Solve through substitution:
7y^2+xy=5
77y+x=57

List the 2 solutions.

well the answer is supposed to be 2 fraction solutions for example (107 over 5, 105 over 5) and (110 over 5 and 115 over 5)

Answer 1

7 y ² + (57 - 77y)(y) = 5
7 y ² + 57y - 77y ² = 5
70 y ² - 57y + 5 = 0
(10y - 1)(7y - 5) = 0
y = 1/10 , y = 5/7

x = 57 - (77) (1/10)
x = 570/10 - 77/10
x = 493/10

x = 57 - (77) (5/7)
x = 399/7 - 385/7
x = 14/7
x = 2

x = 2 , y = 5/7
x = 493/10 , y = 1/10

Answer 2

Eq. 1: 7y^2+xy=5
Eq. 2: 77y+x=57

From Eq. 2, x = 57 - 77y

Substituting the expression for x into Eq. 1:
7y^2 + (57 - 77y) y = 5

7y^2 + 57y - 77y^2 = 5

-70y^2 +57y - 5 = 0

Note that the resulting equation is of the form:
ay^2 + by + c = 0
and so the quadratic formula can be applied:

y = ( -b +- sqrt (b^2 - 4ac) ) / 2a

Applying the quadratic formula:

y = ( -57 +- sqrt (57^2 - 4*(-70)*(-5)) ) / 2 * (-70)
y = ( -57 +- sqrt (3249 - 1400) ) / -140
y = ( -57 +- 43 ) / -140

Solve for the two cases:
When -43 is added to -57:
y = ( -57 + 43 ) / -140
y = -14 / -140
y = 1/10

when -43 is subtracted from -57:
y = ( -57 - 43 ) / -140
y = -100 / -140
y = 5/7

Since x = 57 - 77y,
when y = 1/10,
x = 57 - 77*(1/10)
x = 57 - 7 7/10
x = 49 3/10

when y = 5/7,
x = 57 - 77*(5/7)
x = 57 - 55
x = 2

Therefore, the solution sets are (49 3/10, 1/10) and (2, 5/7).

Check by substituting in the answers in the two equations. You should get an equality.

Answer 3

7y^2 + xy = 5 (1)
77y + x = 57 (2)

using (2):
x = 57 - 77y (subs to 1)

7y^2 + (57 - 77y ) y = 5
7y^2 + 57y - 77y^2 = 5
-72y^2 + 57y - 5 = 0

use quadratic equation:

y = -57 +/- sqrt (57^2 - 4 (-72)(-5) ) / 2 (-72)

y = 0.1005
y = 0.6912

using y = 0.1005:

77(0.1005) + x = 57
x = 49.2615

using y = 0.6912:

77(0.6912) + x = 57
x = 3.7776

Answer 4

I tried it but i ended up with 3 different variables.

I don't think you can do that but don't take my word for it ( I am in 10th grade math, but see what other answers people give you )

Srry.