Question: Solve this system of equations by using substitution.
y = 3x + 1
2y - x = 12
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1. **State the problem:** Solve the system of equations using substitution:
$$y = 3x + 1$$
$$2y - x = 12$$
2. **Use substitution:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = 3x + 1$ into the second equation.
$$2(3x + 1) - x = 12$$
3. **Simplify the equation:**
$$6x + 2 - x = 12$$
$$5x + 2 = 12$$
4. **Isolate $x$:**
$$5x = 12 - 2$$
$$5x = 10$$
$$x = \frac{\cancel{5}x}{\cancel{5}} = \frac{10}{5}$$
$$x = 2$$
5. **Find $y$ by substituting $x = 2$ back into the first equation:**
$$y = 3(2) + 1$$
$$y = 6 + 1$$
$$y = 7$$
6. **Final answer:**
The solution to the system is
$$(2, 7)$$