Answer:
Option 4 - (8,3)
Step-by-step explanation:
Given : The system of equations,
[tex]5r+7s=61[/tex] ......(1)
and [tex]-5r+7s=-19[/tex]......(2)
To find : Which ordered pair (r, s) is the solution to the given system of equations?
Solution :
To get the solution we solve both the equations,
Add equation (1) and (2),
[tex]5r+7s+(-5r+7s)=61+(-19)[/tex]
[tex]5r+7s-5r+7s=61-19[/tex]
[tex]14s=42[/tex]
[tex]s=\frac{42}{14}[/tex]
[tex]s=3[/tex]
Substitute the value of s in equation (1),
[tex]5r+7(3)=61[/tex]
[tex]5r+21=61[/tex]
[tex]5r=61-21[/tex]
[tex]5r=40[/tex]
[tex]r=8[/tex]
The value of r=8 and s=3.
So, ordered pair (8,3) is the solution to the given system of equations.
Therefore, option 4 is correct.
