Final answer:
To solve the system of equations using substitution, start by solving one equation for one variable and then substitute that expression into the other equation. Finally, simplify and solve for the variables.
Step-by-step explanation:
To solve the system of equations using substitution, we can start by solving one equation for one variable and then substituting that expression into the other equation. In this case, we can solve the equation y = x + 1 for x: x = y - 1.
Next, we substitute this expression for x into the other equation: y = 3(y - 1) - 7.
Simplifying the equation gives us: y = 3y - 3 - 7. Combining like terms, we get: y = 3y - 10. Subtracting 3y from both sides, we have: -2y = -10. Finally, dividing both sides by -2, we find: y = 5.
Substituting this value of y back into the equation x = y - 1, we get: x = 5 - 1 = 4.
Therefore, the solution to the system of equations is x = 4 and y = 5.