Answer:
Option D
Step-by-step explanation:
Method 1:
For these kind of MCQ's we test the ordered pair that is given and insert it into both our equations if the left hand side equals the right hand side then the ordered pair is the solution to both the equations
Method 2:
We can also find out the ordered pair ourselves by solving this system of linear equations by different methods either by
Elimination (where we try to eliminate one variable to find out the other)
Substitution (where we substitute one variable in the form of another variable)
Graphing (where we graph both the equations and if they intersect at one common point that is the solution of our system)
We use the Elimination method because its quick and simple so here goes,
[tex]x+y=4\\x-y=-6\\[/tex]
If we add both the equations the variable y will be eliminated like this,
[tex]x+x+y+(-y)=4+(-6)\\2x+0=-2\\2x=-2\\x=-2/2\\x=-1[/tex]
Now we found the value of x = -1 now we need value of y we find the value of y by inserting the value of x in any equation that is given like this,
[tex]x+y=4\\(-1)+y=4\\-1+y=4\\y=4+1\\y=5\\[/tex]
Now the value of y is y = 5 ,
Since our ordered pair is the same as given in the question that is ( -1 , 5)
It is the solution to the system because it makes both equations true.
So option A and option B are also correct but the best out of all these 4 options is Option D so the answer is Option D
