For this one, you'll need to start by solving for a variable. I would use the second equation because x does not have a coefficient with it.
x + 4y = 10
You'll need to isolate the variable by subtracting 4y from both sides of the equation (you always do the opposite operation of what it's currently doing to get rid of it).
x = 10 - 4y
Now you know what x equals, so you are able to substitute 10 - 4y in for x in the first equation.
3(10 - 4y) - 5y = 13
You need to distribute the 3 to the values inside of the parenthesis. 3x10 and 3x4y
30 - 12y - 5y = 13
I like to change subtraction to addition to eliminate errors.
30 + -12y + -5y = 13
Now you want to try to get the variables by themselves, by subtracting 30 from both sides.
-12y + -5y = -17
Combine your like terms by adding the y's together. Two negatives added together make a larger negative.
-17y = -17
Now you will divide each side by -17 so y is isolated. A negative divided by a negative always gives you a positive.
y = 1
Now that you know what y equals, you can substitute that value into your original equation to solve for the value of x.
x + 4y = 10
x + 4(1) = 10
x + 4 = 10
Subtract 4 from both sides to isolate the variable x.
x = 6
Check you solutions using the equation 3x - 5y = 13 given y = 1 and x = 6
3(6) - 5(1) = 13
18 - 5 = 13
13 = 13
