Use substitution method to solve x-2y-5=0, 3x-5y=8

To solve the system of equations using the substitution method, we'll start by solving one equation for one variable and then substituting that expression into the other equation.

Let's solve the first equation, x - 2y - 5 = 0, for x:

x - 2y - 5 = 0
x = 2y + 5

Now, we substitute this expression for x into the second equation, 3x - 5y = 8:

3(2y + 5) - 5y = 8
6y + 15 - 5y = 8
y + 15 = 8
y = 8 - 15
y = -7

Now that we have the value of y, we can substitute it back into the equation we found for x earlier:

x = 2y + 5
x = 2(-7) + 5
x = -14 + 5
x = -9

Therefore, the solution to the system of equations is x = -9 and y = -7.

To do substitution method, we choose an equation and express one of the variables in terms of the other, and finally substitute this to the other equation.

In this case, let's choose the first given equation and express x in terms of y:
x - 2y - 5 = 0
x = 2y + 5
then we substitute this to the second equation:
3x - 5y = 8
3(2y + 5) - 5y = 8
6y + 15 - 5y = 8
y = 8 - 15
y = -7
finally, we substitute this value of x to get y:
x = 2(-7) + 5
x = -14 + 5
x = -9

hope this helps~ :)