Question: A. System d
B. System c
C. System a
D. System b
9. Use substitution to solve this linear system.
x = 2y - 56
5x + 13y = 410
A. (4, -30) B. (4, 30) C. (-4, -30) D. (-4, 30)
top-center graph: a coordinate grid is partially visible with a slanted line segment rising to the right and a vertical axis marked near -8, with the graph extending off the top edge.User:
1. **Problem:** Use substitution to solve the linear system.
$$x = 2y - 56$$
$$5x + 13y = 410$$
2. **Substitute** the expression for $x$ into the second equation.
$$5(2y - 56) + 13y = 410$$
3. **Distribute** the $5$.
$$10y - 280 + 13y = 410$$
4. **Combine like terms**.
$$23y - 280 = 410$$
5. **Add** $280$ to both sides.
$$23y = 690$$
6. **Divide** both sides by $23$.
$$\frac{\cancel{23}y}{\cancel{23}} = \frac{690}{23}$$
$$y = 30$$
7. **Substitute** $y = 30$ into $x = 2y - 56$.
$$x = 2(30) - 56$$
$$x = 60 - 56$$
$$x = 4$$
8. **Solution:** The ordered pair is
$$\boxed{(4, 30)}$$
So the correct answer is **B. $(4, 30)$**.