Question

For each ordered pair, determine whether it is a solution to 7x - 4y = -5.(x,y)(-2,6) it is a solution yes or no(1,3) it is a solution yes or no(-3,4) it is a solution yes or no(4,2) it is a solution yes or no

Answer 1

To determine if an ordered pair is a solution to the equation 7x - 4y = -5, substitute the values of x and y into the equation and check if the equation holds true. The solutions to the equation are (1, 3).

Step-by-step explanation:

To determine if an ordered pair (x, y) is a solution to the equation 7x - 4y = -5, substitute the values of x and y into the equation and check if the equation holds true.

1. For the ordered pair (-2, 6):
2. 7(-2) - 4(6) = -5
3. 
   
4. -14 - 24 = -5
5. 
   
6. -38 = -5This is not true, so (-2, 6) is not a solution.
7. For the ordered pair (1, 3):
8. 7(1) - 4(3) = -5
9. 
   
10. 7 - 12 = -5
11. 
    
12. -5 = -5This is true, so (1, 3) is a solution.
13. For the ordered pair (-3, 4):
14. 7(-3) - 4(4) = -5
15. 
    
16. -21 - 16 = -5
17. 
    
18. -37 = -5This is not true, so (-3, 4) is not a solution.
19. For the ordered pair (4, 2):
20. 7(4) - 4(2) = -5
21. 
    
22. 28 - 8 = -5
23. 
    
24. 20 = -5This is not true, so (4, 2) is not a solution.

Therefore, the solutions to the equation 7x - 4y = -5 are (1, 3).

Answer 2

If x=1, then:

`\begin{gathered} 7(1)-4y=-5 \\ \Rightarrow-4y=-5-7=-12 \\ \Rightarrow y=(-12)/(-4)=3 \\ \\ y=3 \end{gathered}`

therefore, a solution to the equation 7x-4y=-5 is (1,3)