I need help with this asap?!? 5x-6y=16 and 5x+y=2 Systems of equations: substitution method?

5x - 6y = 16 (1)
5x + y = 2 (2)

Consider Equation (2).
5x + y = 2

Subtract 5x from both sides of the equation.
5x - 5x + y = 2 - 5x
y = 2 - 5x (3)

Substitute the y-value in Equation (3) into Equation (1).
5x - 6y = 16
5x - 6(2 - 5x) = 16

Simplify.
5x - 12 + 30x = 16

Combine like terms.
35x - 12 = 16

Add 12 to both sides of the equation.
35x - 12 = 16
35x - 12 + 12 = 16 + 12

Simplify.
35x = 28

Divide both sides of the equation by 35.
35x = 28
35x/35 = 28/35
x = 28/35 = 4/5 = 0.8 This is the value of the x-variable.

Substitute the x-value into Equation (3) to find the y-value.
y = 2 - 5x
y = 2 - 5(0.8)
y = 2 - 4
y = - 2 This is the value of the y-variable.

CHECK
Check the results by substituting them into Equation (1).
5x - 6y = 16
5(0.8) - 6(- 2) = 16
4 + 12 = 16
16 = 16

The above identity indicates that the values x = 0.8 and y = - 2 are correct.

-7y = 14
y = -2
x = 4/5

Substitution:
5x-6y=16 eq(1)
5x+y=2 eq (2)

From eq (2): Rearrange to solve for x, knowing y
y=2-5x

Substitute into eq (1):

5x-6(2-5x)=16
5x-12+30x=16
5x+30x=16+12
35x=28
x=28/35
x=4/5

Substitute x=4/5 into eq (2)

5(4/5) +y=2
4+y=2
y=2-4
y=-2

Thus:
x=4/5
y=-2

5x-6y=16..........[1]
5x+y=2.............[2]

// It would have been simpler to solve by elimination because you have
// identical terms in [1] and [2] that can be quickly eliminated.
// However, to solve by substitution, rewrite [2] solving for y
5x+y=2.............[2]
y = -5x+2..........[2a]

// Now substitute for y from [2a] into [1] and solve for x
5x-6y=16..........[1]
5x - 6(-5x+2) = 16
5x + 30x - 12 = 16
35x = 28
x = 28/35
x = 4/5.............[3]

// Now substitute for x from [3] into [2a] and solve for y
y = -5x+2..........[2a]
y = -5(4/5) + 2
y = -4+2
y = -2..............[4]

Solution is (x,y) = (4/5, -2)............ANS

CHECK YOUR ANSWER
5x-6y= 5(4/5) - 6(-2) = 4+12 = 16..........CORRECT
5x+y= 5(4/5) + (-2) = 4-2 = 2................CORRECT

Substitution method is to find either x= or y= and substitute that into the other equation.

5x +y =2 is a prime candidate.
subtract 5x
y = (-5x +2)
put that into 5x -6(y) =16

5x -6(-5x +2) = 16 <<substitution into other equation
now expand, combine & solve

5x +30x -12 = 16
35x = 28
x = 28/35 = (7/7)(4/5)
x = 4/5