Question: Solve the system of equations using substitution:
y = 3x + 5
2x + 3y = 4
○ (0, 5)
○ (-1, 2)
○ (1, 8)
○ (-2, -1)
1. **State the problem:** We need to solve the system of equations using substitution:
$$y = 3x + 5$$
$$2x + 3y = 4$$
2. **Substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = 3x + 5$ into the second equation.
3. Substitute:
$$2x + 3(3x + 5) = 4$$
4. Expand the terms:
$$2x + 9x + 15 = 4$$
5. Combine like terms:
$$11x + 15 = 4$$
6. Subtract 15 from both sides:
$$11x + \cancel{15} - \cancel{15} = 4 - 15$$
$$11x = -11$$
7. Divide both sides by 11:
$$\frac{11x}{\cancel{11}} = \frac{-11}{\cancel{11}}$$
$$x = -1$$
8. Substitute $x = -1$ back into the first equation to find $y$:
$$y = 3(-1) + 5 = -3 + 5 = 2$$
9. **Solution:** The solution to the system is $(-1, 2)$.
10. **Check the multiple-choice options:**
- (0, 5) no
- (-1, 2) yes
- (1, 8) no
- (-2, -1) no
**Final answer:** $(-1, 2)$