Answer:
D) (1,8)
Step-by-step explanation:
1. Solve 5x + y = 13 for y.
- [tex]5x + y = 13[/tex]
- [tex]5x + y - 5x = 13 - 5x[/tex]
- [tex]y = -5x + 13[/tex]
2. Substitute -5x + 13 for y in 10x - 3y = -14.
- [tex]10x-3y=-14[/tex]
- [tex]10x-3(-5x+13)=-14[/tex]
- [tex]25x-39=-14[/tex]
- [tex]25x - 39 + 39 = -14 + 39[/tex]
- [tex]25x = 25[/tex]
- [tex]\frac{25x}{25} = \frac{25}{25}[/tex]
- [tex]x = 1[/tex]
3. Alright, we now have our x-coordinate, so the point looks like this so far: (1,y).
4. Substitute 1 for x in y = -5x + 13
- [tex]y = -5x + 13[/tex]
- [tex]y=-5(1)+13[/tex]
- [tex]y = -5 + 13[/tex]
- [tex]y = 8[/tex]
5. Okay, we have our x-coordinate and y-coordinate, so the point will look like this: (1,8).
Therefore, the intersection of the two lines is at (1,8).
