1. Solve the system $y = 3x - 5$ and $5x + 4y = -3$. Substitute $y$ from the first equation into the second: $$5x + 4(3x - 5) = -3$$ $$5x + 12x - 20 = -3$$ $$17x - 20 = -3$$ $$17x = 17$$ $$x = 1$$ Find $y$: $$y = 3(1) - 5 = 3 - 5 = -2$$ Solution: $(x,y) = (1, -2)$. 2. Solve the system $x = 2y - 1$ and $7x + 2y = 25$. Substitute $x$ into the second equation: $$7(2y - 1) + 2y = 25$$ $$14y - 7 + 2y = 25$$ $$16y - 7 = 25$$ $$16y = 32$$ $$y = 2$$ Find $x$: $$x = 2(2) - 1 = 4 - 1 = 3$$ Solution: $(x,y) = (3, 2)$. 3. Solve the system $2x + y = 5$ and $x - 2y = 5$. Multiply the second equation by 2 to align $y$ terms: $$2(x - 2y) = 2(5)$$ $$2x - 4y = 10$$ Subtract the first equation from this: $$(2x - 4y) - (2x + y) = 10 - 5$$ $$2x - 4y - 2x - y = 5$$ $$-5y = 5$$ $$y = -1$$ Find $x$: $$2x + (-1) = 5$$ $$2x = 6$$ $$x = 3$$ Solution: $(x,y) = (3, -1)$. 4. Solve the system $2x - 3y = 11$ and $x - y = 4$. Multiply the second equation by 3: $$3(x - y) = 3(4)$$ $$3x - 3y = 12$$ Subtract the first equation from this: $$(3x - 3y) - (2x - 3y) = 12 - 11$$ $$3x - 3y - 2x + 3y = 1$$ $$x = 1$$ Find $y$: $$1 - y = 4$$ $$-y = 3$$ $$y = -3$$ Solution: $(x,y) = (1, -3)$. Each system represents two lines; their solution is the intersection point. Desmos functions for each system: 1. $y = 3x - 5$ and $y = \frac{-5x - 3}{4}$ 2. $y = \frac{x + 1}{2}$ and $7x + 2y = 25$ 3. $y = 5 - 2x$ and $y = \frac{x - 5}{2}$ 4. $y = x - 4$ and $y = \frac{2x - 11}{3}$