Solve Systems 0917Bc

1. **Problem Statement:** Solve the systems of equations given. --- ### a. System: $$\begin{cases} 2x - 4y = 20 \\ x = 4 \end{cases}$$ 2. **Step 1:** Substitute $x = 4$ into the first equation: $$2(4) - 4y = 20$$ 3. **Step 2:** Simplify: $$8 - 4y = 20$$ 4. **Step 3:** Isolate $y$: $$-4y = 20 - 8$$ $$-4y = 12$$ 5. **Step 4:** Divide both sides by $-4$: $$y = \frac{12}{-4}$$ $$y = -3$$ 6. **Answer for (a):** $$x = 4, \quad y = -3$$ --- ### b. System: $$\begin{cases} y = 6x + 11 \\ 2x - 3y = 7 \end{cases}$$ 7. **Step 1:** Substitute $y = 6x + 11$ into the second equation: $$2x - 3(6x + 11) = 7$$ 8. **Step 2:** Expand: $$2x - 18x - 33 = 7$$ 9. **Step 3:** Combine like terms: $$-16x - 33 = 7$$ 10. **Step 4:** Isolate $x$: $$-16x = 7 + 33$$ $$-16x = 40$$ 11. **Step 5:** Divide both sides by $-16$: $$x = \frac{40}{-16}$$ $$x = -\frac{5}{2}$$ 12. **Step 6:** Substitute $x = -\frac{5}{2}$ back into $y = 6x + 11$: $$y = 6\left(-\frac{5}{2}\right) + 11$$ $$y = -15 + 11$$ $$y = -4$$ 13. **Answer for (b):** $$x = -\frac{5}{2}, \quad y = -4$$