Final answer:
To solve the given system of equations using substitution, we first solve one equation for one variable and then substitute that expression into the other equation. By following these steps, we find that the solution to the system is x = 4 and y = -5.
Step-by-step explanation:
To solve the system of equations using substitution, we need to solve one equation for one variable and then substitute that expression into the other equation.
Given the system:
x = 3y + 19
3x - 2y = 22
Step 1: Solve one equation for x or y. Let's solve the first equation for x:
x = 3y + 19
Step 2: Substitute the expression for x into the second equation:
3(3y + 19) - 2y = 22
Step 3: Simplify and solve for y:
9y + 57 - 2y = 22
7y + 57 = 22
7y = -35
y = -5
Step 4: Substitute the value of y back into the first equation to find x:
x = 3(-5) + 19
x = -15 + 19
x = 4
The solution to the system of equations is x = 4 and y = -5.