Solve by elimination 3x + 4y = 10 and 2x - 4y = 5

Problem: Solve the system of linear equations by elimination: $3x + 4y = 10$ and $2x - 4y = 5$.

Steps

1. Add the two equations to eliminate $y$
   $$(3x + 4y) + (2x - 4y) = 10 + 5$$
2. Combine like terms
   $$5x = 15$$
3. Divide both sides by 5
   $$x = 3$$
4. Substitute $x = 3$ into the first equation
   $$3(3) + 4y = 10$$
5. Simplify the multiplication
   $$9 + 4y = 10$$
6. Subtract 9 from both sides
   $$4y = 1$$
7. Divide both sides by 4
   $$y = \frac{1}{4}$$