Question: Solve the system of equations.
-5x + 13y = -7
5x + 4y = 24
x =
y =
1. **State the problem:** Solve the system of linear equations:
$$-5x + 13y = -7$$
$$5x + 4y = 24$$
2. **Add the two equations to eliminate $x$: **
$$(-5x + 13y) + (5x + 4y) = -7 + 24$$
This simplifies to:
$$-5x + 5x + 13y + 4y = 17$$
$$0x + 17y = 17$$
$$17y = 17$$
3. **Solve for $y$: **
$$y = \frac{17}{17}$$
$$y = 1$$
4. **Substitute $y=1$ into the second original equation to solve for $x$: **
$$5x + 4(1) = 24$$
$$5x + 4 = 24$$
$$5x = 24 - 4$$
$$5x = 20$$
5. **Divide both sides by 5 to isolate $x$: **
$$x = \frac{20}{5}$$
$$x = 4$$
**Final answer:**
$$x = 4, \quad y = 1$$