solve equation for y to obtain the slope-intercept form of the equation
So, it seems as though you've either combined two different equations or miss-stated a single equation. In either case, what you've put can yield three different answers. In all cases, the slope-intercept form is a typical way of representing an equation such that slope and y-intercepts on a 2D cartesian plot can be easily extracted. Slope-intercept form is y=mx+b where m is the slope of the line and b is the y-intercept when x=0.
First case: 5x+y=14
subtract 5x from each side: 5x+y-5x=14-5x
simplify and rearrage for form: y=-5x+14 (answer)
Second case: 10x-y=14
subtract 10x from each side: 10x-y-10x=14-10x
simplify and rearrage: -y=-10x+14
mulitply both sides by -1 to get positive y: (-1)*-y=(-1)*(-10x+14)
Third case: 5x+y=10x-y
subtract 5x from both sides: 5x+y-5x=10x-y-5x
add y to both sides: y+y=5x-y+y
divide by 2 on both sides: y=5/2x (answer)
This is probably a little too much detail, but you can see that the process is the same each time. Isolate y on one side by adding/subtracting/multiplying/dividing by numbers or multiples of x. Don't worry about the order you do these in or whether you do an extra operation. You can always get to the same end. You'll Finally, rearrange to get common form, if necessary.
An equation cannot have two equal to ( = ) sign. Can you please rewrite the question on which you need help.