1. **Problem 1:** Find $x$ when $y = -x + 3$ and $y = 2$. 2. Since both expressions equal $y$, set them equal to each other: $$-x + 3 = 2$$ 3. Solve for $x$: $$-x + 3 = 2$$ $$-x = 2 - 3$$ $$-x = -1$$ $$\cancel{-}x = \cancel{-}1$$ $$x = 1$$ **Answer:** $x = 1$. --- 1. **Problem 2:** Solve the simultaneous equations: $$x + y = 5$$ $$2x + y = 7$$ 2. Subtract the first equation from the second to eliminate $y$: $$(2x + y) - (x + y) = 7 - 5$$ $$2x + y - x - y = 2$$ $$x = 2$$ 3. Substitute $x=2$ into the first equation: $$2 + y = 5$$ $$y = 5 - 2$$ $$y = 3$$ **Answer:** $x=2$, $y=3$. --- 1. **Problem 3:** Solve for $a$ and $b$ given: $$a - 3b = -9$$ $$-a + 5b = 13$$ 2. Add the two equations to eliminate $a$: $$(a - 3b) + (-a + 5b) = -9 + 13$$ $$a - 3b - a + 5b = 4$$ $$2b = 4$$ $$b = 2$$ 3. Substitute $b=2$ into the first equation: $$a - 3(2) = -9$$ $$a - 6 = -9$$ $$a = -9 + 6$$ $$a = -3$$ **Answer:** $a = -3$, $b = 2$. --- 1. **Problem 4:** Solve: $$-8x = 72$$ 2. Divide both sides by $-8$: $$\cancel{-8}x = 72$$ $$\cancel{-8}$$ $$x = \frac{72}{-8}$$ $$x = -9$$ **Answer:** $x = -9$. --- 1. **Problem 5:** Twelve times a number equals 108. (a) Let the number be $n$. The equation is: $$12n = 108$$ (b) Solve for $n$: $$n = \frac{108}{12}$$ $$n = 9$$ **Answer:** $n = 9$.