1. Let's solve the system by adding the equations to eliminate one variable. 2. Consider the system: $$4x - y = 3$$ $$6x + y = 7$$ 3. Add the two equations: $$(4x - y) + (6x + y) = 3 + 7$$ $$4x - y + 6x + y = 10$$ $$10x = 10$$ 4. Solve for $x$: $$x = \frac{10}{10} = 1$$ 5. Substitute $x = 1$ into the first equation: $$4(1) - y = 3$$ $$4 - y = 3$$ $$-y = 3 - 4 = -1$$ $$y = 1$$ 6. **Answer:** $x=1, y=1$ --- 1. Now solve the system: $$3x - 5y = -2$$ $$4x + 5y = 9$$ 2. Add the two equations to eliminate $y$: $$(3x - 5y) + (4x + 5y) = -2 + 9$$ $$7x = 7$$ 3. Solve for $x$: $$x = \frac{7}{7} = 1$$ 4. Substitute $x=1$ into the first equation: $$3(1) - 5y = -2$$ $$3 - 5y = -2$$ $$-5y = -5$$ $$y = 1$$ 5. **Answer:** $x=1, y=1$ --- 1. Solve: $$3x - 2y = -3$$ $$3x + 2y = 9$$ 2. Add the two equations: $$(3x - 2y) + (3x + 2y) = -3 + 9$$ $$6x = 6$$ 3. Solve for $x$: $$x = \frac{6}{6} = 1$$ 4. Substitute $x=1$ into the first: $$3(1) - 2y = -3$$ $$3 - 2y = -3$$ $$-2y = -6$$ $$y = 3$$ 5. **Answer:** $x=1, y=3$ --- 1. Solve: $$4a - 7b = -3$$ $$3a + 7b = 10$$ 2. Add the two equations: $$(4a - 7b) + (3a + 7b) = -3 + 10$$ $$7a = 7$$ 3. Solve for $a$: $$a = \frac{7}{7} = 1$$ 4. Substitute $a=1$ into the first: $$4(1) - 7b = -3$$ $$4 - 7b = -3$$ $$-7b = -7$$ $$b = 1$$ 5. **Answer:** $a=1, b=1$ --- 1. Solve: $$-x - 3y = -7$$ $$x - 2y = 2$$ 2. Add both equations: $$(-x - 3y) + (x - 2y) = -7 + 2$$ $$-5y = -5$$ 3. Solve for $y$: $$y = \frac{-5}{-5} = 1$$ 4. Substitute $y=1$ into the second equation: $$x - 2(1) = 2$$ $$x - 2 = 2$$ $$x = 4$$ 5. **Answer:** $x=4, y=1$ --- 1. Solve: $$4m + g = -22$$ $$4m + 2g = -3$$ 2. Subtract the first from the second: $$(4m + 2g) - (4m + g) = -3 - (-22)$$ $$4m + 2g - 4m - g = 19$$ $$g = 19$$ 3. Substitute $g=19$ into the first: $$4m + 19 = -22$$ $$4m = -41$$ $$m = -\frac{41}{4}$$ 4. **Answer:** $m = -\frac{41}{4}, g = 19$