Final answer:
To solve the system of equations x = 2y + 7 and 3x - 2y = 3 using substitution, solve for one variable and substitute it into the other equation. The solution is x = -2 and y = -9/2.
Step-by-step explanation:
To solve the system of equations x = 2y + 7 and 3x - 2y = 3 by substitution, we can solve one equation for x or y and substitute it into the other equation.
Let's solve the first equation x = 2y + 7 for x:
x - 2y = 7
Now, substitute x in the second equation with 2y + 7:
3(2y + 7) - 2y = 3
Simplify and solve for y:
6y + 21 - 2y = 3
4y + 21 = 3
4y = -18
y = -18/4 = -9/2
Now, substitute y back into the first equation to solve for x:
x = 2(-9/2) + 7
x = -9 + 7 = -2
The solution to the system of equations x = 2y + 7 and 3x - 2y = 3 is x = -2 and y = -9/2.