I need help solving these problems by using the substitution problem

2x-3y=16
5x+2y=21

substitution is a method, not a problem (though it appears to be a problem for you! :-)

taking the first equation, solve for x or y:

x = (16+3y)/2

now "substitute" that into the other equation

5(16+3y)/2 + 2y = 21
80+15y + 4y = 42
19y = -38
y = -2
so, x = (16-6)/2 = 5

check that (5,-2) fits both original equations, just to be sure

To solve this system of equations using the substitution method, you can follow these steps:

Step 1: Solve one equation for one variable in terms of the other variable.

Let's solve the first equation for x:
2x - 3y = 16

Add 3y to both sides:
2x = 3y + 16

Divide both sides by 2:
x = (3y + 16)/2

Step 2: Substitute the expression obtained in Step 1 into the other equation.

Let's substitute x = (3y + 16)/2 into the second equation:
5x + 2y = 21

Replace x with (3y + 16)/2:
5((3y + 16)/2) + 2y = 21

Step 3: Simplify the equation obtained in Step 2 and solve for y.

5(3y + 16)/2 + 2y = 21
(15y + 80)/2 + 2y = 21
(15y + 80) + 4y = 42 (multiply through by 2 to eliminate the fraction)

Simplify and combine like terms:
15y + 80 + 4y = 42
19y + 80 = 42
19y = 42 - 80
19y = -38
y = -38/19
y = -2

Step 4: Substitute the value of y back into either of the original equations to solve for x.

Let's substitute y = -2 into the first equation:
2x - 3(-2) = 16
2x + 6 = 16
2x = 16 - 6
2x = 10
x = 10/2
x = 5

So the solution to the system of equations is x = 5 and y = -2.