Solve by Substitution method.

15x-20y=-7
15y=4+5x

1) Solve the first equation for either variable.

2) Every where in the second equation that the solved-for variable appears, replace it with the value it is equal to.

3) You now have only 1 variable in the second equation. Solve the second equation for that variable and you will get a numeric value for it.

4) Every where in either of the original equations that the variable you just found a numeric value for exists, plug in the numeric value instead.

5) You can now solve that equation for the other variable, obtaining a numeric value for it also.

5x-15y=4

To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute it into the other equation. Let's start by solving one equation for one variable.

Equation 1: 15x - 20y = -7
Equation 2: 15y = 4 + 5x

Let's solve Equation 2 for y:
Divide both sides of Equation 2 by 15 to isolate y:
15y/15 = (4 + 5x)/15
y = (4 + 5x)/15

Now we substitute this value of y into Equation 1:
15x - 20((4 + 5x)/15) = -7

Simplify the equation:
15x - (20/15)(4 + 5x) = -7
15x - (4/3 + 4x/3) = -7
15x - (4/3) - (4x/3) = -7

Now, we'll combine like terms and solve for x:
(15x - 4/3) - (4x/3) = -7
(15x - 4 - 4x)/3 = -7

Multiply both sides by 3 to eliminate the fraction:
(15x - 4 - 4x) = -21

Combine like terms:
11x - 4 = -21

Add 4 to both sides:
11x = -17

Divide both sides by 11 to solve for x:
x = -17/11

Now that we have the value of x, we can substitute it back into Equation 2 to find the value of y:
15y = 4 + 5(-17/11)
15y = 4 - 85/11
15y = (44 - 85)/11
15y = -41/11

Divide both sides by 15 to solve for y:
y = -41/11 * (1/15)
y = -41/165

Therefore, the solution to the system of equations is x = -17/11 and y = -41/165.