Solve the following system of equations.?

Question

5x - y = 7
2 + x = 7y

Answer 1

For the 2nd equation, bring the 7y over the left hand side and 2 onto the right hand side: x - 7y= -2
5x - y= 7
x - 7y= -2
Multiply the whole 2nd equation by 5: 5(x - 7y= -2)
5x - y= 7
5x - 35y= -10
Now, subtract the equations to get rid of the x variable.
-y - (-35y) = 7 - (-10)
34y= 17
y= 17/34 or 1/2
Replace the y variable with 1/2 in the first equation:
5x - 1/2= 7
5x= 15/2
x= 15/10 or 3/2

Answer 2

5 x - y = 7
2 + x = 7y

I would solve the second equation for x
2 + x = 7 y
Subtract 2 from both sides
x = 7y- 2

Now Substitue this into the first equation
5x - y = 7
5(7y-2)-y = 7
Distribute
35y- 10 - y = 7
Combine like terms
34 y - 10 = 7
Add 10 to both sides
34 y = 17
Divide by 34
y = 1/2

Now substitue this value into the second equation
2 + x = 7y
2 + x = 7(1/2)
2 + x = 7/2= 3 1/2
x = 3 1/2 - 2
x = 1 1/2

(1 1/2, 1/2)

Answer 3

5x - y = 7.......Eq 1
2 + x = 7y.......Eq 2
Consider Eq 1
5x - y = 7
5x = 7 + y
x = (7 + y)/5
Substitute the derived value of 'x' in Eq 2
2 + x = 7y
2 + (7 + y)/5 = 7y
10 + 7 + y = (7y)(5)
17 + y = 35y
35y = 17 + y
35y - y = 17
34y = 17
y = 17/34
y = 1/2
Substitute the value of y in Eq 1
5x - y = 7
5x - 1/2 = 7
5x = 7+(1/2)
5x = 15/2
x = 15/10
x = 3/2

Answer 4

5x-y=7

2+x=7y
-2 -2
_______
x=7y-2
5(7y-2)-y=7
35y-10-y=7
+10 +10
____________
34y=17
y= .5

2+x=7*.5
2+x=3.5
-2 -2
_______
x=1.5

answer is (1.5, .5)

Answer 5

5x-y=7
y=5x-7

7y+x=-2
x=7y-2

x=35x-51
-34x-51

7y=119/34

x=51/34
y=119/298