6x=7y=2 8x+5y=20

To solve the system of equations:

6x = 7y - 2
8x + 5y = 20

We can use the method of substitution or elimination. Let's use the method of substitution:

Step 1: Solve one equation for one variable in terms of the other variable. From the first equation, isolate x:

6x = 7y - 2
Divide both sides by 6:
x = (7y - 2) / 6

Step 2: Substitute the expression for x into the other equation. Replace x with (7y - 2) / 6 in the second equation:

8x + 5y = 20
8((7y - 2) / 6) + 5y = 20

Step 3: Simplify and solve for y:

Multiply both sides by 6 to get rid of the fraction:
8(7y - 2) + 30y = 120
56y - 16 + 30y = 120
86y - 16 = 120
86y = 136
y = 136 / 86
y ≈ 1.581

Step 4: Substitute the value of y back into either of the original equations to solve for x. Let's use the first equation:

6x = 7y - 2
6x = 7(1.581) - 2
6x = 11.067 - 2
6x = 9.067
x = 9.067 / 6
x ≈ 1.511

Therefore, the solution to the system of equations is approximately x ≈ 1.511 and y ≈ 1.581.